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3  The Functional Equation of Zeta Distributions Associated With NonEuclidean Jordan Algebras Ben Saïd, Salem
This paper is devoted to the study of certain zeta distributions
associated with simple nonEuclidean Jordan algebras. An explicit
form of the corresponding functional equation and Bernsteintype
identities is obtained.


23  Constructing Representations of Finite Simple Groups and Covers DabbaghianAbdoly, Vahid
Let $G$ be a finite group and $\chi$ be an irreducible character of $G$. An efficient
and simple method to construct representations of finite groups is applicable
whenever $G$ has a subgroup $H$ such that $\chi_H$
has a linear constituent with multiplicity $1$.
In this paper we show (with a few exceptions) that if $G$
is a simple group or a covering group of a simple group and
$\chi$ is an irreducible character of $G$ of degree less than 32,
then there exists a subgroup $H$ (often a Sylow subgroup) of $G$
such that $\chi_H$ has a linear constituent with multiplicity $1$.


39  $C^*$Algebras of Irreversible Dynamical Systems Exel, R.; Vershik, A.
We show that certain $C^*$algebras which have been studied by,
among others, Arzumanian, Vershik, Deaconu, and Renault, in
connection with a measurepreserving transformation of a measure space
or a covering map of a compact space, are special cases of the
endomorphism crossedproduct construction recently introduced by the
first named author. As a consequence these algebras are given
presentations in terms of generators and relations. These results
come as a consequence of a general theorem on faithfulness of
representations which are covariant with respect to certain circle
actions. For the case of topologically free covering maps we prove a
stronger result on faithfulness of representations which needs no
covariance. We also give a necessary and sufficient condition for
simplicity.


64  Multiplicity Results for Nonlinear Neumann Problems Filippakis, Michael; Gasiński, Leszek; Papageorgiou, Nikolaos S.
In this paper we study nonlinear elliptic problems of Neumann type driven by the
$p$Laplac\ian differential operator. We look for situations guaranteeing the existence
of multiple solutions. First we study problems which are strongly resonant at infinity
at the first (zero) eigenvalue. We prove five multiplicity results, four for problems
with nonsmooth potential and one for problems with a $C^1$potential. In the last part,
for nonsmooth problems in which the potential eventually exhibits a strict
super$p$growth under a symmetry condition, we prove the existence of infinitely
many pairs of nontrivial solutions. Our approach is variational based on the critical
point theory for nonsmooth functionals. Also we present some results concerning the first
two elements of the spectrum of the negative $p$Laplacian with Neumann boundary condition.


93  Motivic Haar Measure on Reductive Groups Gordon, Julia
We define a motivic analogue of the Haar measure for groups of the form
$G(k\llp t\rrp)$, where~$k$ is an algebraically closed field
of characteristic zero, and $G$ is a reductive algebraic group defined over
$k$.
A classical Haar measure on such groups does not
exist since they are not locally compact.
We use the theory of motivic integration introduced by M.~Kontsevich to
define an additive function on a certain natural Boolean algebra of subsets of
$G(k\llp t\rrp)$. This function takes values in the socalled dimensional
completion of
the Grothendieck ring of the category of varieties over the base
field. It is invariant under translations by all elements of $G(k\llp t\rrp)$,
and therefore we call it a motivic analogue of Haar measure.
We give an explicit construction of the motivic Haar measure, and then prove
that the result is independent of all the choices that are made in the process.


115  Quelques résultats sur les équations $ax^p+by^p=cz^2$ Ivorra, W.; Kraus, A.
Let $p$ be a prime number $\geq 5$ and $a,b,c$ be non
zero natural numbers. Using the works of K. Ribet and A. Wiles on the
modular representations, we get new results about the description of
the primitive solutions of the diophantine equation $ax^p+by^p=cz^2$,
in case the product of the prime divisors of $abc$ divides $2\ell$,
with $\ell$ an odd prime number. For instance, under some conditions
on $a,b,c$, we provide a constant $f(a,b,c)$ such that there are no
such solutions if $p>f(a,b,c)$. In application, we obtain information
concerning the $\Q$rational points of hyperelliptic curves given by
the equation $y^2=x^p+d$ with $d\in \Z$.


154  Singular Integrals on Product Spaces Related to the Carleson Operator Prestini, Elena
We prove $L^p(\mathbb T^2)$ boundedness, $1<p\leq 2$, of
variable coefficients singular integrals that generalize the double
Hilbert transform and present two phases that may be of very rough
nature. These operators are involved in problems of a.e. convergence
of double Fourier series, likely in the role played by the Hilbert
transform in the proofs of a.e. convergence of one dimensional Fourier
series. The proof due to C.Fefferman provides a basis for our method.


180  Infinite Dimensional Representations of Canonical Algebras Reiten, Idun; Ringel, Claus Michael
The
aim of this paper is to extend the structure theory for infinitely
generated modules over tame hereditary algebras to the more
general case of modules over concealed canonical algebras. Using
tilting, we may assume that we deal with canonical algebras. The
investigation is centered around the generic and the Pr\"{u}fer
modules, and how other modules are determined by these
modules.


225  Generalized Reductive Lie Algebras: Connections With Extended Affine Lie Algebras and Lie Tori Azam, Saeid
We investigate a class of Lie algebras which we call {\it generalized reductive
Lie algebras}. These are generalizations of semisimple, reductive, and affine
KacMoody Lie algebras. A generalized reductive Lie algebra which has an irreducible
root system is said to be {\it irreducible\/} and we note that this class of algebras
has been under intensive investigation in recent years. They have also been called
{\it extended affine Lie algebras}. The larger class of generalized reductive Lie
algebras has not been so intensively investigated. We study them in this paper and note
that one way they arise is as fixed point subalgebras of finite order automorphisms. We
show that the core modulo the center of a generalized reductive Lie algebra is a direct
sum of centerless Lie tori. Therefore one can use the results known about the
classification of centerless Lie tori to classify the cores modulo centers of
generalized reductive Lie algebras.


249  Convergence of FourierPadé Approximants for Stieltjes Functions Bello Hernández, M.; Mínguez Ceniceros, J.
We prove convergence of diagonal multipoint Pad\'e approximants of
Stieltjestype functions when a certain moment problem is
determinate. This is used for the study of the convergence of
FourierPad\'e and nonlinear FourierPad\'e approximants for such
type of functions.


262  Connections on a Parabolic Principal Bundle Over a Curve Biswas, Indranil
The aim here is to define connections on a parabolic
principal bundle. Some applications are given.


282  Nonreductive Homogeneous PseudoRiemannian Manifolds of Dimension Four Fels, M. E.; Renner, A. G.
A method, due to \'Elie Cartan, is used to give an algebraic
classification of the nonreductive homogeneous pseudoRiemannian
manifolds of dimension four. Only one case with Lorentz signature can
be Einstein without having constant curvature, and two cases with
$(2,2)$ signature are Einstein of which one is Ricciflat. If a
fourdimensional nonreductive homogeneous pseudoRiemannian manifold
is simply connected, then it is shown to be diffeomorphic to
$\reals^4$. All metrics for the simply connected nonreductive
Einstein spaces are given explicitly. There are no nonreductive
pseudoRiemannian homogeneous spaces of dimension two and none of
dimension three with connected isotropy subgroup.


312  Partie imaginaire des résonances de Rayleigh dans le cas d'une boule Gamblin, Didier
Nous \'etudions les r\'esonances de Rayleigh cr\'e\'ees par
une boule en dimension deux
et trois. Nous savons qu'elles convergent exponentiellement vite vers l'axe
r\'eel. Nous calculons
exactement les fonctions r\'esonantes associ\'ees puis nous les estimons
asymptotiquement en fonction
de la partie r\'eelle des r\'esonances. L'application de la formule de
Green nous donne alors le taux
de d\'ecroissance exponentielle de la partie imaginaire des r\'esonances.


344  Reducibility for $SU_n$ and Generic Elliptic Representations Goldberg, David
We study reducibility of representations
parabolically induced from discrete series
representations of $SU_n(F)$ for $F$ a $p$adic field of
characteristic zero. We use the approach of studying the relation
between $R$groups when a reductive subgroup of a quasisplit group
and the full group have the same derived group. We use restriction to
show the quotient of $R$groups is in natural bijection with a group
of characters. Applying this to $SU_n(F)\subset U_n(F)$ we show the
$R$ group for $SU_n$ is the semidirect product of an $R$group for
$U_n(F)$ and this group of characters. We derive results on
nonabelian $R$groups and generic elliptic representations as well.


362  Cohomology Pairings on the Symplectic Reduction of Products Goldin, R. F.; Martin, S.
Let $M$ be the product of two compact Hamiltonian
$T$spaces $X$ and $Y$. We present a formula for evaluating
integrals on the symplectic reduction of $M$ by the diagonal $T$
action. At every regular value of the moment map for $X\times Y$, the
integral is the convolution of two distributions associated to the
symplectic reductions of $X$ by $T$ and of $Y$ by $T$. Several
examples illustrate the computational strength of this relationship.
We also prove a linear analogue which can be used to find cohomology
pairings on toric orbifolds.


381  Extremal Metric for the First Eigenvalue on a Klein Bottle Jakobson, Dmitry; Nadirashvili, Nikolai; Polterovich, Iosif
The first eigenvalue of the Laplacian on a surface can be viewed
as a functional on the space of Riemannian metrics of a given
area. Critical points of this functional are called extremal
metrics. The only known extremal metrics are a round sphere, a
standard projective plane, a Clifford torus and an equilateral
torus. We construct an extremal metric on a Klein bottle. It is a
metric of revolution, admitting a minimal isometric embedding into
a sphere ${\mathbb S}^4$ by the first eigenfunctions. Also, this
Klein bottle is a bipolar surface for Lawson's
$\tau_{3,1}$torus. We conjecture that an extremal metric for the
first eigenvalue on a Klein bottle is unique, and hence it
provides a sharp upper bound for $\lambda_1$ on a Klein bottle of
a given area. We present numerical evidence and prove the first
results towards this conjecture.


401  On Pointwise Estimates of Positive Definite Functions With Given Support Kolountzakis, Mihail N.; Révész, Szilárd Gy.
The following problem has been suggested by Paul Tur\' an. Let
$\Omega$ be a symmetric convex body in the Euclidean space $\mathbb R^d$
or in the torus $\TT^d$. Then, what is the largest possible value
of the integral of positive definite functions that are supported
in $\Omega$ and normalized with the value $1$ at the origin? From
this, Arestov, Berdysheva and Berens arrived at the analogous
pointwise extremal problem for intervals in $\RR$. That is, under
the same conditions and normalizations, the supremum of possible
function values at $z$ is to be found for any given point
$z\in\Omega$. However, it turns out that the problem for the real
line has already been solved by Boas and Kac, who gave several
proofs and also mentioned possible extensions to $\RR^d$ and to
nonconvex domains as well.


419  Stark's Conjecture and New Stickelberger Phenomena Snaith, Victor P.
We introduce a new conjecture concerning the construction
of elements in the annihilator ideal
associated to a Galois action on the higherdimensional algebraic
$K$groups of rings of integers in number fields. Our conjecture is
motivic in the sense that it involves the (transcendental) Borel
regulator as well as being related to $l$adic \'{e}tale
cohomology. In addition, the conjecture generalises the wellknown
CoatesSinnott conjecture. For example, for a totally real
extension when $r = 2, 4, 6, \dotsc$ the CoatesSinnott
conjecture merely predicts that zero annihilates $K_{2r}$ of the
ring of $S$integers while our conjecture predicts a nontrivial
annihilator. By way of supporting evidence, we prove the
corresponding (conjecturally equivalent) conjecture for the Galois
action on the \'{e}tale cohomology of the cyclotomic extensions of
the rationals.


449  Existence and Multiplicity of Positive Solutions for Singular Semipositone $p$Laplacian Equations Agarwal, Ravi P.; Cao, Daomin; Lü, Haishen; O'Regan, Donal
Positive solutions are obtained for the boundary value problem
\[\begin{cases}
(  u' ^{p2}u')'
=\lambda f( t,u),\;t\in ( 0,1) ,p>1\\
u( 0) =u(1) =0.
\end{cases}
\]
Here $f(t,u) \geq M,$ ($M$ is a positive constant)
for $(t,u) \in [0\mathinner{,}1] \times (0,\infty )$.
We will show the existence of two positive
solutions by using degree theory together with the upperlower
solution method.


476  Apolar Schemes of Algebraic Forms Chipalkatti, Jaydeep
This is a note on the classical Waring's problem for algebraic forms.
Fix integers $(n,d,r,s)$, and let $\Lambda$ be a general $r$dimensional
subspace of degree $d$ homogeneous polynomials in $n+1$ variables. Let
$\mathcal{A}$ denote the variety of $s$sided polar polyhedra of $\Lambda$.
We carry out a casebycase study of the structure of $\mathcal{A}$ for several
specific values of $(n,d,r,s)$. In the first batch of examples, $\mathcal{A}$ is
shown to be a rational variety. In the second batch, $\mathcal{A}$ is a
finite set of which we calculate the cardinality.}


492  Extension Theorems on Weighted Sobolev Spaces and Some Applications Chua, SengKee
We extend the extension theorems to weighted Sobolev spaces
$L^p_{w,k}(\mathcal D)$ on $(\varepsilon,\delta)$ domains with doubling weight $w$
that satisfies a Poincar\'e inequality and such that $w^{1/p}$ is locally
$L^{p'}$. We also make use of the main theorem to improve weighted
Sobolev interpolation inequalities.


529  On the Group of Homeomorphisms of the Real Line That Map the Pseudoboundary Onto Itself Dijkstra, Jan J.; Mill, Jan van
In this paper we primarily consider two natural subgroups of the autohomeomorphism group of the real
line $\R$, endowed with the compactopen topology. First, we prove that the subgroup of
homeomorphisms that map the set of rational numbers $\Q$ onto itself
is homeomorphic to the infinite power of $\Q$ with
the product topology. Secondly, the group consisting of homeomorphisms that map the pseudoboundary
onto itself is shown to be homeomorphic to the hyperspace of nonempty compact subsets of $\Q$ with
the Vietoris topology. We obtain similar results for the Cantor set but we also prove that these
results do not extend to $\R^n$ for $n\ge 2$, by linking the groups in question with Erd\H os
space.


548  Hausdorff and QuasiHausdorff Matrices on Spaces of Analytic Functions Galanopoulos, P.; Papadimitrakis, M.
We consider Hausdorff and quasiHausdorff matrices as operators
on classical spaces of analytic functions such as the Hardy and
the Bergman spaces, the Dirichlet space, the Bloch spaces and $\BMOA$. When the generating
sequence of the matrix is the moment sequence of a measure $\mu$,
we find the conditions on $\mu$ which are equivalent to the boundedness
of the matrix on the various spaces.


580  Annihilators for the Class Group of a Cyclic Field of Prime Power Degree, II Greither, Cornelius; Kučera, Radan
We prove, for a field $K$ which is cyclic of odd prime power
degree over the rationals, that the annihilator of the
quotient of the units of $K$ by a suitable large subgroup (constructed
from circular units) annihilates what we call the
nongenus part of the class group.
This leads to stronger annihilation results for the whole
class group than a routine application of the RubinThaine method
would produce, since the
part of the class group determined by genus theory has an obvious
large annihilator which is not detected by
that method; this is our reason for concentrating on
the nongenus part. The present work builds on and strengthens
previous work of the authors; the proofs are more conceptual now,
and we are also able to construct an example which demonstrates
that our results cannot be easily sharpened further.


600  Geometric Study of Minkowski Differences of Plane Convex Bodies MartinezMaure, Yves
In the Euclidean plane $\mathbb{R}^{2}$, we define the Minkowski difference
$\mathcal{K}\mathcal{L}$ of two arbitrary convex bodies $\mathcal{K}$,
$\mathcal{L}$ as a rectifiable closed curve $\mathcal{H}_{h}\subset \mathbb{R}
^{2}$ that is determined by the difference $h=h_{\mathcal{K}}h_{\mathcal{L}
} $ of their support functions. This curve $\mathcal{H}_{h}$ is
called the
hedgehog with support function $h$. More generally, the object of hedgehog
theory is to study the BrunnMinkowski theory in the vector space of
Minkowski differences of arbitrary convex bodies of Euclidean space $\mathbb{R}
^{n+1}$, defined as (possibly singular and selfintersecting) hypersurfaces
of $\mathbb{R}^{n+1}$. Hedgehog theory is useful for: (i)
studying convex bodies by splitting them into a sum in order to reveal their
structure; (ii) converting analytical problems into
geometrical ones by considering certain real functions as support
functions.
The purpose of this paper is to give a detailed study of plane
hedgehogs, which constitute the basis of the theory. In particular:
(i) we study their length measures and solve the extension of the
ChristoffelMinkowski problem to plane hedgehogs; (ii) we
characterize support functions of plane convex bodies among support
functions of plane hedgehogs and support functions of plane hedgehogs among
continuous functions; (iii) we study the mixed area of
hedgehogs in $\mathbb{R}^{2}$ and give an extension of the classical Minkowski
inequality (and thus of the isoperimetric inequality) to hedgehogs.


625  A Steinberg Cross Section for NonConnected Affine KacMoody Groups Mohrdieck, Stephan
In this paper we generalise the concept of a Steinberg
cross section to nonconnected affine KacMoody groups.
This Steinberg cross section is a section to the
restriction of the adjoint quotient map to a given exterior
connected component of the affine KacMoody group.
(The adjoint quotient is only defined on a certain submonoid of the
entire group, however, the intersection of this submonoid with each
connected component is nonvoid.)
The image of the Steinberg cross section consists of a
``twisted Coxeter cell'',
a transversal slice to a twisted Coxeter element.
A crucial point in the proof of the main result is that the image of
the cross section can be endowed with a $\Cst$action.


643  Centralizers and Twisted Centralizers: Application to Intertwining Operators Yu, Xiaoxiang
ABSTRACT
The equality of the centralizer and twisted centralizer is proved
based on a casebycase analysis when the unipotent radical of a
maximal parabolic subgroup is abelian.
Then this result is used to determine the poles of intertwining operators.


673  The Generalized Cuspidal Cohomology Problem Bart, Anneke; Scannell, Kevin P.
Let $\Gamma \subset \SO(3,1)$ be a lattice.
The well known bending deformations, introduced by
\linebreak Thurston
and Apanasov, can be used
to construct nontrivial curves of representations of $\Gamma$
into $\SO(4,1)$ when $\Gamma \backslash \hype{3}$ contains
an embedded totally geodesic surface. A tangent vector to such a
curve is given by a nonzero group cohomology class
in $\H^1(\Gamma, \mink{4})$. Our main result generalizes this
construction of cohomology to the context of ``branched''
totally geodesic surfaces.
We also consider a natural generalization of the famous
cuspidal cohomology problem for the Bianchi groups
(to coefficients in nontrivial representations), and
perform calculations in a finite range.
These calculations lead directly to an interesting example of a
link complement in $S^3$
which is not infinitesimally rigid in $\SO(4,1)$.
The first order deformations of this link complement are supported
on a piecewise totally geodesic $2$complex.


691  Hypoelliptic BiInvariant Laplacians on Infinite Dimensional Compact Groups Bendikov, A.; SaloffCoste, L.
On a compact connected group $G$, consider the infinitesimal
generator $L$ of a central symmetric Gaussian convolution
semigroup $(\mu_t)_{t>0}$. Using appropriate notions of distribution
and smooth function spaces, we prove that $L$ is hypoelliptic if and only if
$(\mu_t)_{t>0} $ is absolutely continuous with respect to Haar measure
and admits a continuous density $x\mapsto \mu_t(x)$, $t>0$, such that
$\lim_{t\ra 0} t\log \mu_t(e)=0$. In particular, this condition holds
if and only if any Borel measure $u$ which is solution of $Lu=0$
in an open set $\Omega$ can be represented by a continuous
function in $\Omega$. Examples are discussed.


726  On Value Distribution Theory of Second Order Periodic ODEs, Special Functions and Orthogonal Polynomials Chiang, YikMan; Ismail, Mourad E. H.
We show that the value distribution (complex oscillation) of
solutions of certain periodic second order ordinary differential
equations studied by Bank, Laine and Langley is closely
related to confluent hypergeometric functions, Bessel functions
and Bessel polynomials. As a result, we give a complete
characterization of the zerodistribution in the sense of
Nevanlinna theory of the solutions for two classes of the ODEs.
Our approach uses special functions and their asymptotics. New
results concerning finiteness of the number of zeros
(finitezeros) problem of Bessel and Coulomb wave functions with
respect to the parameters are also obtained as a consequence. We
demonstrate that the problem for the remaining class of ODEs not
covered by the above ``special function approach" can be
described by a classical Heine problem for differential
equations that admit polynomial solutions.


768  Decomposability of von Neumann Algebras and the Mazur Property of Higher Level Hu, Zhiguo; Neufang, Matthias
The decomposability
number of a von Neumann algebra $\m$ (denoted by $\dec(\m)$) is the
greatest cardinality of a family of pairwise orthogonal nonzero
projections in $\m$. In this paper, we explore the close
connection between $\dec(\m)$ and the cardinal level of the Mazur
property for the predual $\m_*$ of $\m$, the study of which was
initiated by the second author. Here, our main focus is on
those von Neumann algebras whose preduals constitute such
important Banach algebras on a locally compact group $G$ as the
group algebra $\lone$, the Fourier algebra $A(G)$, the measure
algebra $M(G)$, the algebra $\luc^*$, etc. We show that for
any of these von Neumann algebras, say $\m$, the cardinal number
$\dec(\m)$ and a certain cardinal level of the Mazur property of $\m_*$
are completely encoded in the underlying group structure. In fact,
they can be expressed precisely by two dual cardinal
invariants of $G$: the compact covering number $\kg$ of $G$ and
the least cardinality $\bg$ of an open basis at the identity of
$G$. We also present an application of the Mazur property of higher
level to the topological centre problem for the Banach algebra
$\ag^{**}$.


796  MordellWeil Groups and the Rank of Elliptic Curves over Large Fields Im, BoHae
Let $K$ be a number field, $\overline{K}$ an algebraic closure of
$K$ and $E/K$ an elliptic curve
defined over $K$. In this paper, we prove that if $E/K$ has a
$K$rational point $P$ such that $2P\neq O$ and $3P\neq O$, then
for each $\sigma\in \Gal(\overline{K}/K)$, the MordellWeil group
$E(\overline{K}^{\sigma})$ of $E$ over the fixed subfield of
$\overline{K}$ under $\sigma$ has infinite rank.


820  Diametrically Maximal and Constant Width Sets in Banach Spaces Moreno, J. P.; Papini, P. L.; Phelps, R. R.
We characterize diametrically maximal and constant width
sets in $C(K)$, where $K$ is any compact Hausdorff space. These
results are applied to prove that the sum of two diametrically
maximal sets needs not be diametrically maximal, thus solving a
question raised in a paper by Groemer. A~characterization of
diametrically maximal sets in $\ell_1^3$ is also given, providing
a negative answer to Groemer's problem in finite dimensional
spaces. We characterize constant width sets in $c_0(I)$, for
every $I$, and then we establish the connections between the Jung
constant of a Banach space and the existence of constant width
sets with empty interior. Porosity properties of families of sets
of constant width and rotundity properties of diametrically
maximal sets are also investigated. Finally, we present some
results concerning nonreflexive and Hilbert spaces.


843  On the OneLevel Density Conjecture for Quadratic Dirichlet LFunctions Õzlük, A. E.; Snyder, C.
In a previous article, we studied the distribution of ``lowlying"
zeros of the family of quad\ratic Dirichlet $L$functions assuming
the Generalized Riemann Hypothesis for all Dirichlet
$L$functions. Even with this very strong assumption, we were
limited to using weight functions whose Fourier transforms are
supported in the interval $(2,2)$. However, it is widely believed
that this restriction may be removed, and this leads to what has
become known as the OneLevel Density Conjecture for the zeros of
this family of quadratic $L$functions. In this note, we make use
of Weil's explicit formula as modified by Besenfelder to prove an
analogue of this conjecture.


859  Nonstandard Ideals from Nonstandard Dual Pairs for $L^1(\omega)$ and $l^1(\omega)$ Read, C. J.
The Banach convolution algebras $l^1(\omega)$
and their continuous counterparts $L^1(\bR^+,\omega)$
are much
studied, because (when the submultiplicative weight function
$\omega$ is radical) they are pretty much the prototypic examples
of commutative radical Banach algebras. In cases of ``nice''
weights $\omega$, the only closed ideals they have are the obvious,
or ``standard'', ideals. But in the
general case, a brilliant but very difficult paper of Marc Thomas
shows that nonstandard ideals exist in $l^1(\omega)$. His
proof was successfully exported to the continuous case
$L^1(\bR^+,\omega)$ by Dales and McClure, but remained
difficult. In this paper we first present a small improvement: a
new and easier proof of the existence of nonstandard ideals in
$l^1(\omega)$ and $L^1(\bR^+,\omega)$. The new proof is based on
the idea of a ``nonstandard dual pair'' which we introduce.
We are then able to make a much larger improvement: we
find nonstandard ideals in $L^1(\bR^+,\omega)$ containing functions
whose supports extend all the way down to zero in $\bR^+$, thereby solving
what has become a notorious problem in the area.


877  Functorial Decompositions of Looped Coassociative Co$H$ Spaces Selick, P.; Theriault, S.; Wu, J.
Selick and Wu gave a functorial decomposition of
$\Omega\Sigma X$ for pathconnected, $p$local \linebreak$\CW$\nbdcom\plexes $X$
which obtained the smallest nontrivial functorial retract $A^{\min}(X)$
of $\Omega\Sigma X$. This paper uses methods developed by
the second author in order to extend such functorial
decompositions to the loops on coassociative co$H$ spaces.


897  Distributions invariantes sur les groupes réductifs quasidéployés Courtès, François
Soit $F$ un corps local non archim\'edien, et $G$ le groupe des
$F$points d'un groupe r\'eductif connexe quasid\'eploy\'e d\'efini sur $F$.
Dans cet article, on s'int\'eresse aux distributions sur $G$ invariantes
par conjugaison, et \`a l'espace de leurs restrictions \`a l'alg\`ebre de
Hecke $\mathcal{H}$ des fonctions sur $G$ \`a support compact
biinvariantes par un sousgroupe d'Iwahori $I$ donn\'e. On montre tout
d'abord que les valeurs d'une telle distribution sur $\mathcal{H}$
sont enti\`erement d\'etermin\'ees par sa restriction au sousespace de
dimension finie des \'el\'ements de $\mathcal{H}$ \`a support dans la
r\'eunion des sousgroupes parahoriques de $G$ contenant $I$. On utilise
ensuite cette propri\'et\'e pour montrer, moyennant certaines conditions
sur $G$, que cet espace est engendr\'e d'une part par certaines
int\'egrales orbitales semisimples, d'autre part par les int\'egrales
orbitales unipotentes, en montrant tout d'abord des r\'esultats
analogues sur les groupes finis.


1000  On the Cohomology of Moduli of Vector Bundles and the Tamagawa Number of $\operatorname{SL}_n$ Dhillon, Ajneet
We compute some Hodge and Betti numbers of the moduli space of stable rank $r$,
degree $d$ vector bundles on a smooth projective curve. We
do not assume $r$ and $d$ are coprime.
In the process we equip the cohomology of an arbitrary algebraic stack with a
functorial mixed Hodge structure. This Hodge structure is
computed in the case of the moduli stack of rank $r$, degree
$d$ vector bundles on a curve. Our methods also yield a formula
for the Poincar\'e
polynomial of the moduli stack that is valid over any
ground field. In the last section we use the previous sections
to give a proof that the Tamagawa number of $\sln$ is one.


1026  Karamata Renewed and Local Limit Results Handelman, David
Connections between behaviour of real analytic functions (with no
negative Maclaurin series coefficients and radius of convergence one)
on the open unit interval, and to a lesser extent on arcs of the unit
circle, are explored, beginning with Karamata's approach. We develop
conditions under which the asymptotics of the coefficients are related
to the values of the function near $1$; specifically, $a(n)\sim
f(11/n)/ \alpha n$ (for some positive constant $\alpha$), where
$f(t)=\sum a(n)t^n$. In particular, if $F=\sum c(n) t^n$ where $c(n)
\geq 0$ and $\sum c(n)=1$, then $f$ defined as $(1F)^{1}$ (the
renewal or Green's function for $F$) satisfies this condition if $F'$
does (and a minor additional condition is satisfied). In come cases,
we can show that the absolute sum of the differences of consecutive
Maclaurin coefficients converges. We also investigate situations in
which less precise asymptotics are available.


1095  A CasselmanShalika Formula for the Shalika Model of $\operatorname{GL}_n$ Sakellaridis, Yiannis
The CasselmanShalika method is a way to compute explicit
formulas for periods of irreducible unramified representations of
$p$adic groups that are associated to unique models (i.e.,
multiplicityfree induced representations). We apply this method
to the case of the Shalika model of $GL_n$, which is known to
distinguish lifts from odd orthogonal groups. In the course of our
proof, we further develop a variant of the method, that was
introduced by Y. Hironaka, and in effect reduce many such problems
to straightforward calculations on the group.


1121  The Feichtinger Conjecture for Wavelet Frames, Gabor Frames and Frames of Translates Bownik, Marcin; Speegle, Darrin
The Feichtinger conjecture is considered for three special families of
frames. It is shown that if a wavelet frame satisfies a certain weak
regularity condition, then it can be written as the finite union of
Riesz basic sequences each of which is a wavelet system. Moreover, the
above is not true for general wavelet frames. It is also shown that a
supadjoint Gabor frame can be written as the finite union of Riesz
basic sequences. Finally, we show how existing techniques can be
applied to determine whether frames of translates can be written as
the finite union of Riesz basic sequences. We end by giving an example
of a frame of translates such that any Riesz basic subsequence must
consist of highly irregular translates.


1144  Partial $*$Automorphisms, Normalizers, and Submodules in Monotone Complete $C^*$Algebras Hamana, Masamichi
For monotone complete $C^*$algebras
$A\subset B$ with $A$ contained in $B$ as a monotone closed
$C^*$subalgebra, the relation $X = AsA$
gives a bijection between the set of all
monotone closed linear subspaces $X$ of $B$ such that
$AX + XA \subset X$
and
$XX^* + X^*X \subset A$
and a set of certain partial
isometries $s$ in the ``normalizer" of $A$ in $B$,
and similarly for the map $s \mapsto \Ad s$
between the latter set and a set of certain ``partial $*$automorphisms"
of $A$.
We introduce natural inverse semigroup
structures in the set of such $X$'s and the set of
partial $*$automorphisms of $A$, modulo a certain relation, so that
the composition of these maps induces an inverse semigroup
homomorphism between them.
For a large enough $B$ the homomorphism becomes surjective and
all the partial $*$automorphisms of
$A$ are realized via partial isometries in $B$.
In particular, the inverse semigroup associated with
a type ${\rm II}_1$ von Neumann factor,
modulo the outer automorphism group,
can be viewed as the fundamental group of the factor.
We also consider the $C^*$algebra version of these results.


1203  Orbites unipotentes et pôles d'ordre maximal de la fonction $\mu $ de HarishChandra Heiermann, Volker
Dans un travail ant\'erieur, nous
avions montr\'e que l'induite parabolique (normalis\'ee) d'une
repr\'esentation irr\'eductible cuspidale $\sigma $ d'un
sousgroupe de Levi $M$ d'un groupe $p$adique contient un
sousquotient de carr\'e int\'egrable, si et seulement si la
fonction $\mu $ de HarishChandra a un p\^ole en $\sigma $ d'ordre
\'egal au rang parabolique de $M$. L'objet de cet article est
d'interpr\'eter ce r\'esultat en termes de fonctorialit\'e de
Langlands.


1229  Intégrales orbitales tordues sur $\GL(n,F)$ et corps locaux proches\,: applications Henniart, Guy; Lemaire, Bertrand
Soient $F$ un corps
commutatif localement compact non archim\'edien, $G=\GL
(n,F)$ pour un entier $n\geq 2$, et $\kappa$ un caract\`ere de
$F^\times$ trivial sur $(F^\times)^n$. On prouve une formule pour
les $\kappa$int\'egrales orbitales r\'eguli\`eres sur $G$
permettant, si $F$ est de caract\'eristique $>0$, de les relever
\`a la caract\'eristique nulle. On en d\'eduit deux r\'esultats
nouveaux en caract\'eristique $>0$\,: le ``lemme fondamental'' pour
l'induction automorphe, et une version simple de la formule des
traces tordue locale d'Arthur reliant $\kappa$int\'egrales
orbitales elliptiques et caract\`eres $\kappa$tordus. Cette
formule donne en particulier, pour une s\'erie
$\kappa$discr\`ete de $G$, les $\kappa$int\'egrales orbitales
elliptiques d'un pseudocoefficient comme valeurs du caract\`ere
$\kappa$tordu.


1268  GaugeInvariant Ideals in the $C^*$Algebras of Finitely Aligned HigherRank Graphs Sims, Aidan
We produce a complete description of the lattice of gaugeinvariant
ideals in $C^*(\Lambda)$ for a finitely aligned $k$graph
$\Lambda$. We provide a condition on $\Lambda$ under which every ideal
is gaugeinvariant. We give conditions on $\Lambda$ under which
$C^*(\Lambda)$ satisfies the hypotheses of the KirchbergPhillips
classification theorem.


1291  The General Structure of $G$Graded Contractions of Lie Algebras I. The Classification WeimarWoods, Evelyn
We give the general structure of complex (resp., real) $G$graded
contractions of Lie algebras where $G$ is an arbitrary finite Abelian
group. For this purpose, we introduce a number of concepts, such as
pseudobasis, higherorder identities, and sign invariants. We
characterize the equivalence classes of $G$graded contractions by
showing that our set of invariants (support, higherorder identities,
and sign invariants) is complete, which yields a classification.


1341  Author Index  Index des auteurs 2006, for 2006  pour
No abstract.
