Expand all Collapse all | Results 351 - 375 of 459 |
351. CMB 2006 (vol 49 pp. 256)
A Bernstein--Walsh Type Inequality and Applications A Bernstein--Walsh type inequality for $C^{\infty }$ functions of several
variables is derived, which then is applied to obtain analogs and
generalizations of the following classical theorems: (1) Bochnak--Siciak
theorem: a $C^{\infty }$\ function on $\mathbb{R}^{n}$ that is real
analytic on every line is real analytic; (2) Zorn--Lelong theorem: if a
double power series $F(x,y)$\ converges on a set of lines of positive
capacity then $F(x,y)$\ is convergent; (3) Abhyankar--Moh--Sathaye theorem:
the transfinite diameter of the convergence set of a divergent series is
zero.
Keywords:Bernstein-Walsh inequality, convergence sets, analytic functions, ultradifferentiable functions, formal power series Categories:32A05, 26E05 |
352. CMB 2006 (vol 49 pp. 247)
A Szpilrajn--Marczewski Type Theorem for Concentration Dimension on Polish Spaces Let $X$ be a Polish space.
We will prove that
$$
\dim_T X=\inf \{\dim_L X': X'\text{ is homeomorphic to
} X\},
$$
where $\dim_L X$ and $\dim_T X$ stand
for the concentration dimension and
the topological dimension of $X$, respectively.
Keywords:Hausdorff dimension, topological dimension, LÃ©vy concentration function, concentration dimension Categories:11K55, 28A78 |
353. CMB 2006 (vol 49 pp. 213)
On Inductive Limit Type Actions of the Euclidean Motion Group on Stable UHF Algebras An invariant is presented which classifies, up to
equivariant isomorphism, $C^*$-dynamical systems arising as limits from
inductive systems of elementary $C^*$-algebras on which the Euclidean
motion group acts by way of unitary representations that decompose into
finite direct sums of irreducibles.
Keywords:classification, $C^*$-dynamical system Categories:46L57, 46L35 |
354. CMB 2006 (vol 49 pp. 203)
The Ergodic Hilbert Transform for Admissible Processes It is shown that the ergodic Hilbert transform
exists for a class of bounded symmetric admissible processes
relative to invertible measure preserving transformations. This
generalizes the well-known result on the existence of the ergodic
Hilbert transform.
Keywords:Hilbert transform, admissible processes Categories:28D05, 37A99 |
355. CMB 2006 (vol 49 pp. 11)
Going-Down Results for $C_{i}$-Fields We search for theorems that, given a $C_i$-field $K$ and a subfield $k$ of $K$, allow
us to conclude that $k$ is a $C_j$-field for some $j$. We give appropriate theorems in
the case $K=k(t)$ and $K = k\llp t\rrp$. We then consider the more difficult case where $K/k$
is an algebraic extension. Here we are able to prove some results, and make conjectures. We
also point out the connection between these questions and Lang's conjecture on nonreal function
fields over a real closed field.
Keywords:$C_i$-fields, Lang's Conjecture Categories:12F, 14G |
356. CMB 2006 (vol 49 pp. 55)
Non Abelian Twisted Reidemeister Torsion for Fibered Knots In this article, we give an explicit formula to compute the
non abelian twisted sign-deter\-mined Reidemeister torsion of the
exterior of a fibered knot in terms of its monodromy. As an
application, we give explicit formulae for the non abelian
Reidemeister torsion of torus knots and of the figure eight knot.
Keywords:Reidemeister torsion, Fibered knots, Knot groups, Representation space, $\SU$, $\SL$, Adjoint representation, Monodromy Categories:57Q10, 57M27, 57M25 |
357. CMB 2006 (vol 49 pp. 3)
On a Class of Singular Integral Operators With Rough Kernels In this paper, we study the $L^p$ mapping properties of a class of singular
integral operators with rough kernels belonging to certain block spaces. We
prove that our operators are bounded on $L^p$ provided that their kernels
satisfy a size condition much weaker than that for the classical
Calder\'{o}n--Zygmund singular integral operators. Moreover, we present an
example showing that our size condition is optimal. As a consequence of our
results, we substantially improve a previously known result on certain maximal
functions.
Keywords:Singular integrals, Rough kernels, Square functions,, Maximal functions, Block spaces Categories:42B20, 42B15, 42B25 |
358. CMB 2005 (vol 48 pp. 523)
Angle Measures and Bisectors in Minkowski Planes \begin{abstract}
We prove that a Minkowski plane is Euclidean if and only if Busemann's or
Glogovskij's definitions
of angular bisectors coincide
with a bisector defined by an angular measure in the sense of Brass.
In addition, bisectors defined by the area measure coincide with bisectors
defined by the circumference (arc length) measure
if and only if the unit circle is an
equiframed curve.
Keywords:Radon curves, Minkowski geometry, Minkowski planes,, angular bisector, angular measure, equiframed curves Categories:52A10, 52A21 |
359. CMB 2005 (vol 48 pp. 614)
On Finite-to-One Maps Let $f\colon X\to Y$ be a $\sigma$-perfect $k$-dimensional surjective
map of metrizable spaces such that $\dim Y\leq m$. It is shown that
for every positive integer $p$ with $ p\leq m+k+1$ there exists a
dense $G_{\delta}$-subset ${\mathcal H}(k,m,p)$ of $C(X,\uin^{k+p})$
with the source limitation topology such that each fiber of
$f\triangle g$, $g\in{\mathcal H}(k,m,p)$, contains at most
$\max\{k+m-p+2,1\}$ points. This result
provides a proof the following conjectures of
S. Bogatyi, V. Fedorchuk and J. van Mill.
Let $f\colon X\to Y$ be a $k$-dimensional map between compact
metric spaces with $\dim Y\leq m$. Then:
\begin{inparaenum}[\rm(1)]
\item there exists a map
$h\colon X\to\uin^{m+2k}$ such that $f\triangle h\colon X\to
Y\times\uin^{m+2k}$ is 2-to-one provided $k\geq 1$;
\item there exists a
map $h\colon X\to\uin^{m+k+1}$ such that $f\triangle h\colon X\to
Y\times\uin^{m+k+1}$ is $(k+1)$-to-one.
\end{inparaenum}
Keywords:finite-to-one maps, dimension, set-valued maps Categories:54F45, 55M10, 54C65 |
360. CMB 2005 (vol 48 pp. 580)
Exceptional Sets in Hartogs Domains Assume that $\Omega$ is a Hartogs domain in $\mathbb{C}^{1+n}$,
defined as $\Omega=\{(z,w)\in\mathbb{C}^{1+n}:|z|<\mu(w),w\in H\}$, where $H$ is an open set in
$\mathbb{C}^{n}$ and $\mu$ is a continuous function with positive values in $H$ such that $-\ln\mu$
is a strongly plurisubharmonic function in $H$. Let $\Omega_{w}=\Omega\cap(\mathbb{C}\times\{w\})$.
For a given set $E$ contained in $H$ of the type $G_{\delta}$ we construct a holomorphic function
$f\in\mathbb{O}(\Omega)$ such that
\[
E=\Bigl\{ w\in\mathbb{C}^{n}:\int_{\Omega_{w}}|f(\cdot\,,w)|^{2}\,d\mathfrak{L}^{2}=\infty\Bigr\}.
\]
Keywords:boundary behaviour of holomorphic functions,, exceptional sets Category:30B30 |
361. CMB 2005 (vol 48 pp. 561)
A Note on Lagrangian Loci of Quotients We study Hamiltonian actions of compact groups in the presence of
compatible involutions. We show that the Lagrangian fixed point set
on the symplectically reduced space is isomorphic to the disjoint
union of the involutively reduced spaces corresponding to
involutions on the group strongly inner to the given one.
Our techniques imply that the solution to the eigenvalues of a sum problem
for a given real form can be reduced to the quasi-split real form in the
same inner class. We also consider invariant quotients with respect to
the corresponding real form of the complexified group.
Keywords:Quotients, involutions, real forms, Lagrangian loci Category:53D20 |
362. CMB 2005 (vol 48 pp. 547)
Degeneracy of 2-Forms and 3-Forms We study some global aspects of differential complex 2-forms and 3-forms
on complex manifolds.
We compute the cohomology classes represented by the sets of points
on a manifold where such a form degenerates in various senses,
together with other similar cohomological obstructions.
Based on these results and a formula for projective
representations, we calculate the degree of the projectivization
of certain orbits of the representation $\Lambda^k\C^n$.
Keywords:Classes of degeneracy loci, 2-forms, 3-forms, Thom polynomials, global singularity theory Categories:14N10, 57R45 |
363. CMB 2005 (vol 48 pp. 505)
On the Generalized d'Alembert's and Wilson's Functional Equations on a Compact group Let $G$ be a compact group. Let $\sigma$ be a continuous involution
of $G$. In this paper, we are
concerned by the following functional equation
$$\int_{G}f(xtyt^{-1})\,dt+\int_{G}f(xt\sigma(y)t^{-1})\,dt=2g(x)h(y), \quad
x, y \in G,$$ where $f, g, h \colonG \mapsto \mathbb{C}$, to be
determined, are complex continuous functions on $G$ such that $f$ is
central. This equation generalizes d'Alembert's and Wilson's
functional equations. We show that the solutions are expressed by
means of characters of irreducible, continuous and unitary
representations of the group $G$.
Keywords:Compact groups, Functional equations, Central functions, Lie, groups, Invariant differential operators. Categories:39B32, 39B42, 22D10, 22D12, 22D15 |
364. CMB 2005 (vol 48 pp. 409)
The Existence of Universal Inner Functions on the Unit Ball of $\mathbb{C}^n$ It is shown that there exists an inner function
$I$ defined on the unit ball ${\bf B}^n$ of ${\mathbb C}^n$
such that each function holomorphic on ${\bf B}^n$ and
bounded by $1$ can be approximated by
``non-Euclidean translates" of $I$.
Keywords:universal inner functions Categories:32A35, 30D50, 47B38 |
365. CMB 2005 (vol 48 pp. 340)
Short Geodesics of Unitaries in the $L^2$ Metric Let $\M$ be a type II$_1$ von Neumann algebra, $\tau$ a trace in $\M$,
and $\l2$ the GNS Hilbert space of $\tau$. We regard the unitary group
$U_\M$ as a subset of $\l2$ and characterize the shortest smooth
curves joining two fixed unitaries in the $L^2$ metric. As a
consequence of this we obtain that $U_\M$, though a complete (metric)
topological group, is not an embedded riemannian submanifold of $\l2$
Keywords:unitary group, short geodesics, infinite dimensional riemannian manifolds. Categories:46L51, 58B10, 58B25 |
366. CMB 2005 (vol 48 pp. 180)
Geometry and Arithmetic of Certain Double Octic Calabi--Yau Manifolds We study Calabi--Yau manifolds constructed as double coverings of
$\mathbb{P}^3$ branched along an octic surface. We give a list of 87
examples corresponding to arrangements of eight planes defined over
$\mathbb{Q}$. The Hodge numbers are computed for all examples. There are
10 rigid Calabi--Yau manifolds and 14 families with $h^{1,2}=1$. The
modularity conjecture is verified for all the rigid examples.
Keywords:Calabi--Yau, double coverings, modular forms Categories:14G10, 14J32 |
367. CMB 2005 (vol 48 pp. 283)
Enlarged Inclusion of Subdifferentials This paper studies the integration of inclusion of subdifferentials. Under
various verifiable conditions, we obtain that if two proper lower
semicontinuous functions $f$ and $g$ have the subdifferential of $f$
included in the $\gamma$-enlargement of the subdifferential of $g$, then
the difference of those functions is $ \gamma$-Lipschitz over their
effective domain.
Keywords:subdifferential,, directionally regular function,, approximate convex function,, subdifferentially and directionally stable function Categories:49J52, 46N10, 58C20 |
368. CMB 2005 (vol 48 pp. 267)
Continuous Adjacency Preserving Maps on Real Matrices It is proved that every adjacency preserving continuous map
on the vector space of real matrices of fixed size, is either a
bijective affine tranformation
of the form $ A \mapsto PAQ+R$, possibly followed by the transposition if
the matrices are of square size, or its range is contained
in a linear subspace consisting of matrices of rank at most one
translated by some matrix $R$. The result
extends previously known
theorems where the map was assumed to be also injective.
Keywords:adjacency of matrices, continuous preservers, affine transformations Categories:15A03, 15A04. |
369. CMB 2005 (vol 48 pp. 260)
A Restriction Theorem for a \\$k$-Surface in $\mathbb R ^n$ We establish a sharp Fourier restriction estimate
for a measure on a $k$-surface in $\mathbb R ^n$, where $n=k(k+3)/2$.
Keywords:Fourier restriction Category:42B10 |
370. CMB 2005 (vol 48 pp. 195)
On Suslinian Continua A continuum is said to be Suslinian if it does not contain uncountably
many mutually exclusive nondegenerate subcontinua. We prove that
Suslinian continua are perfectly normal and rim-metrizable. Locally
connected Suslinian continua have weight at most $\omega_1$ and under
appropriate set-theoretic conditions are metrizable. Non-separable
locally connected Suslinian continua are rim-finite on some open set.
Keywords:Suslinian continuum, Souslin line, locally connected, rim-metrizable,, perfectly normal, rim-finite Categories:54F15, 54D15, 54F50 |
371. CMB 2005 (vol 48 pp. 161)
Hankel Convolution Operators on Spaces of Entire Functions of Finite Order In this paper we study Hankel transforms and Hankel convolution
operators on spaces of entire functions of finite order and their
duals.
Keywords:Hankel transform, convolution, entire functions, finite order Category:46F12 |
372. CMB 2005 (vol 48 pp. 147)
Baker-Type Estimates for Linear Forms in the Values of $q$-Series We obtain lower estimates for the absolute values
of linear forms of the values of generalized Heine
series at non-zero points of an imaginary quadratic field~$\II$,
in particular of the values of $q$-exponential function.
These estimates depend on the individual coefficients,
not only on the maximum of their absolute values.
The proof uses a variant of classical Siegel's method
applied to a system of functional Poincar\'e-type equations
and the connection between the solutions of these functional
equations and the generalized Heine series.
Keywords:measure of linear independence, $q$-series Categories:11J82, 33D15 |
373. CMB 2005 (vol 48 pp. 121)
Necessary and Sufficient Conditions for the Central Norm to Equal $2^h$ in the Simple Continued Fraction Expansion of $\sqrt{2^hc}$ for Any Odd $c>1$ |
Necessary and Sufficient Conditions for the Central Norm to Equal $2^h$ in the Simple Continued Fraction Expansion of $\sqrt{2^hc}$ for Any Odd $c>1$ We look at the simple continued fraction expansion of $\sqrt{D}$
for any $D=2^hc $ where $c>1$ is odd with a goal of
determining necessary and
sufficient conditions for the central norm (as determined by
the infrastructure of the underlying real quadratic order therein) to be
$2^h$. At the end of the paper, we also address the case where $D=c$
is odd and the central norm of $\sqrt{D}$ is equal to $2$.
Keywords:quadratic Diophantine equations, simple continued fractions,, norms of ideals, infrastructure of real quadratic fields Categories:11A55, 11D09, 11R11 |
374. CMB 2004 (vol 47 pp. 481)
A New Characterization of Hardy Martingale Cotype Space We give a new characterization of Hardy martingale cotype
property of complex quasi-Banach space by using the existence of a
kind of plurisubharmonic functions. We also characterize the best
constants of Hardy martingale inequalities with values
in the complex quasi-Banach space.
Keywords:Hardy martingale, Hardy martingale cotype,, plurisubharmonic function Categories:46B20, 52A07, 60G44 |
375. CMB 2004 (vol 47 pp. 624)
A Compactness Theorem for Yang-Mills Connections In this paper, we consider Yang-Mills connections
on a vector bundle $E$ over a compact Riemannian manifold $M$ of
dimension $m> 4$, and we show that any set of Yang-Mills
connections with the uniformly bounded $L^{\frac{m}{2}}$-norm of
curvature is compact in $C^{\infty}$ topology.
Keywords:Yang-Mills connection, vector bundle, gauge transformation Categories:58E20, 53C21 |