1. CJM Online first
2. CJM Online first
 De Bernardi, Carlo Alberto; Veselý, Libor

Tilings of normed spaces
By a tiling of a topological linear space $X$ we mean a
covering of $X$ by at least two closed convex sets,
called tiles, whose nonempty interiors are
pairwise disjoint.
Study of tilings of infinitedimensional spaces initiated in
the
1980's with pioneer papers by V. Klee.
We prove some general properties of tilings of locally convex
spaces,
and then apply these results to study existence of tilings of
normed and Banach spaces by tiles possessing
certain smoothness or rotundity properties. For a Banach space
$X$,
our main results are the following.
1. $X$ admits no tiling by FrÃ©chet smooth bounded tiles.
2. If $X$ is locally uniformly rotund (LUR), it does not admit
any tiling by balls.
3. On the other hand, some $\ell_1(\Gamma)$ spaces, $\Gamma$
uncountable, do admit
a tiling by pairwise disjoint LUR bounded tiles.
Keywords:tiling of normed space, FrÃ©chet smooth body, locally uniformly rotund body, $\ell_1(\Gamma)$space Categories:46B20, 52A99, 46A45 

3. CJM 2015 (vol 68 pp. 334)
 Demchenko, Oleg; Gurevich, Alexander

Kernels in the Category of Formal Group Laws
Fontaine described the category of formal groups over the ring
of Witt vectors over a finite field
of characteristic $p$ with the aid of triples consisting of the
module of logarithms,
the DieudonnÃ© module and the morphism from the former to the
latter. We propose
an explicit construction for the kernels in this category in
term of Fontaine's triples.
The construction is applied to the formal norm homomorphism in
the case of an unramified extension
of $\mathbb{Q}_p$ and of a totally ramified extension of degree less
or equal than $p$. A similar
consideration applied to a global extension allows us to establish
the existence of a strict
isomorphism between the formal norm torus and a formal group
law coming from $L$series.
Keywords:formal groups, $p$divisible groups, Dieudonne modules, norm tori Category:14L05 

4. CJM 2013 (vol 66 pp. 373)
 Kim, Sun Kwang; Lee, Han Ju

Uniform Convexity and BishopPhelpsBollobÃ¡s Property
A new characterization of the uniform convexity of
Banach space is obtained in the sense of BishopPhelpsBollobÃ¡s
theorem. It is also proved that the couple of Banach spaces $(X,Y)$
has the bishopphelpsbollobÃ¡s property for every banach space $y$
when $X$ is uniformly convex. As a corollary, we show that the
BishopPhelpsBollobÃ¡s theorem holds for bilinear forms on
$\ell_p\times \ell_q$ ($1\lt p, q\lt \infty$).
Keywords:BishopPhelpsBollobÃ¡s property, BishopPhelpsBollobÃ¡s theorem, norm attaining, uniformly convex Categories:46B20, 46B22 

5. CJM 2012 (vol 66 pp. 102)
 Birth, Lidia; Glöckner, Helge

Continuity of convolution of test functions on Lie groups
For a Lie group $G$, we show that the map
$C^\infty_c(G)\times C^\infty_c(G)\to C^\infty_c(G)$,
$(\gamma,\eta)\mapsto \gamma*\eta$
taking a pair of
test functions to their convolution is continuous if and only if $G$ is $\sigma$compact.
More generally, consider $r,s,t
\in \mathbb{N}_0\cup\{\infty\}$ with $t\leq r+s$, locally convex spaces $E_1$, $E_2$
and a continuous bilinear map $b\colon E_1\times E_2\to F$
to a complete locally convex space $F$.
Let $\beta\colon C^r_c(G,E_1)\times C^s_c(G,E_2)\to C^t_c(G,F)$,
$(\gamma,\eta)\mapsto \gamma *_b\eta$ be the associated convolution map.
The main result is a characterization of those $(G,r,s,t,b)$
for which $\beta$ is continuous.
Convolution
of compactly supported continuous functions on a locally compact group
is also discussed, as well as convolution of compactly supported $L^1$functions
and convolution of compactly supported Radon measures.
Keywords:Lie group, locally compact group, smooth function, compact support, test function, second countability, countable basis, sigmacompactness, convolution, continuity, seminorm, product estimates Categories:22E30, 46F05, 22D15, 42A85, 43A10, 43A15, 46A03, 46A13, 46E25 

6. CJM 2012 (vol 64 pp. 1222)
 Bobiński, Grzegorz

Normality of Maximal Orbit Closures for Euclidean Quivers
Let $\Delta$ be an Euclidean quiver. We prove that the closures of
the maximal orbits in the varieties of representations of $\Delta$
are normal and CohenMacaulay (even complete intersections).
Moreover, we give a generalization of this result for the tame
concealedcanonical algebras.
Keywords:normal variety, complete intersection, Euclidean quiver, concealedcanonical algebra Categories:16G20, 14L30 

7. CJM 2012 (vol 64 pp. 1182)
 Tall, Franklin D.

PFA$(S)[S]$: More Mutually Consistent Topological Consequences of $PFA$ and $V=L$
Extending the work of Larson and Todorcevic,
we show there
is a model of set theory in which normal spaces are collectionwise
Hausdorff if they are either first countable or locally compact, and
yet there are no first countable $L$spaces or compact
$S$spaces. The model is one of the form PFA$(S)[S]$, where $S$
is a coherent Souslin tree.
Keywords:PFA$(S)[S]$, proper forcing, coherent Souslin tree, locally compact, normal, collectionwise Hausdorff, supercompact cardinal Categories:54A35, 54D15, 54D20, 54D45, 03E35, 03E57, 03E65 

8. CJM 2010 (vol 63 pp. 200)
 Rahman, Mizan

An Explicit Polynomial Expression for a $q$Analogue of the 9$j$ Symbols
Using standard transformation and summation formulas for basic
hypergeometric series we obtain an explicit polynomial form of the
$q$analogue of the 9$j$ symbols, introduced by the author in a
recent publication. We also consider a limiting case in which the
9$j$ symbol factors into two Hahn polynomials. The same
factorization occurs in another limit case of the corresponding
$q$analogue.
Keywords:6$j$ and 9$j$ symbols, $q$analogues, balanced and verywellpoised basic hypergeometric series, orthonormal polynomials in one and two variables, Racah and $q$Racah polynomials and their extensions Categories:33D45, 33D50 

9. CJM 2009 (vol 61 pp. 1118)
 Pontreau, Corentin

Petits points d'une surface
Pour toute sousvari\'et\'e g\'eom\'etriquement irr\'eductible $V$
du grou\pe multiplicatif
$\mathbb{G}_m^n$, on sait qu'en dehors d'un nombre fini de
translat\'es de tores exceptionnels
inclus dans $V$, tous les points sont de hauteur minor\'ee par une
certaine quantit\'e $q(V)^{1}>0$. On conna\^it de plus une borne
sup\'erieure pour la somme des degr\'es de ces translat\'es de
tores pour des valeurs de $q(V)$ polynomiales en le degr\'e de $V$.
Ceci n'est pas le cas si l'on exige une minoration quasioptimale
pour la hauteur des points de $V$, essentiellement lin\'eaire en l'inverse du degr\'e.
Nous apportons ici une r\'eponse partielle \`a ce probl\`eme\,: nous
donnons une majoration de la somme des degr\'es de ces translat\'es de
soustores de codimension $1$ d'une hypersurface $V$. Les r\'esultats,
obtenus dans le cas de $\mathbb{G}_m^3$, mais compl\`etement
explicites, peuvent toutefois s'\'etendre \`a $\mathbb{G}_m^n$,
moyennant quelques petites complications inh\'erentes \`a la dimension
$n$.
Keywords:Hauteur normalisÃ©e, groupe multiplicatif, problÃ¨me de Lehmer, petits points Categories:11G50, 11J81, 14G40 

10. CJM 2008 (vol 60 pp. 520)
 Chen, ChangPao; Huang, HaoWei; Shen, ChunYen

Matrices Whose Norms Are Determined by Their Actions on Decreasing Sequences
Let $A=(a_{j,k})_{j,k \ge 1}$ be a nonnegative matrix. In this
paper, we characterize those $A$ for which $\A\_{E, F}$ are
determined by their actions on decreasing sequences, where $E$ and
$F$ are suitable normed Riesz spaces of sequences. In particular,
our results can apply to the following spaces: $\ell_p$, $d(w,p)$,
and $\ell_p(w)$. The results established here generalize
ones given by Bennett; Chen, Luor, and Ou; Jameson; and
Jameson and Lashkaripour.
Keywords:norms of matrices, normed Riesz spaces, weighted mean matrices, NÃ¶rlund mean matrices, summability matrices, matrices with row decreasing Categories:15A60, 40G05, 47A30, 47B37, 46B42 

11. CJM 2007 (vol 59 pp. 966)
 Forrest, Brian E.; Runde, Volker; Spronk, Nico

Operator Amenability of the Fourier Algebra in the $\cb$Multiplier Norm
Let $G$ be a locally compact group, and let $A_{\cb}(G)$ denote the
closure of $A(G)$, the Fourier algebra of $G$, in the space of completely
bounded multipliers of $A(G)$. If $G$ is a weakly amenable, discrete group
such that $\cstar(G)$ is residually finitedimensional, we show that
$A_{\cb}(G)$ is operator amenable. In particular,
$A_{\cb}(\free_2)$ is operator amenable even though $\free_2$, the free
group in two generators, is not an amenable group. Moreover, we show that
if $G$ is a discrete group such that $A_{\cb}(G)$ is operator amenable,
a closed ideal of $A(G)$ is weakly completely complemented in $A(G)$
if and only if it has an approximate identity bounded in the $\cb$multiplier
norm.
Keywords:$\cb$multiplier norm, Fourier algebra, operator amenability, weak amenability Categories:43A22, 43A30, 46H25, 46J10, 46J40, 46L07, 47L25 

12. CJM 2005 (vol 57 pp. 750)
 Sabourin, Hervé

Sur la structure transverse Ã une orbite nilpotente adjointe
We are interested in Poisson structures to
transverse nilpotent adjoint orbits in a complex semisimple Lie algebra,
and we study their polynomial nature. Furthermore, in the case
of $sl_n$,
we construct some families of nilpotent orbits with quadratic
transverse structures.
Keywords:nilpotent adjoint orbits, conormal orbits, Poisson transverse structure Categories:22E, 53D 

13. CJM 2004 (vol 56 pp. 897)
 Borwein, Jonathan M.; Borwein, David; Galway, William F.

Finding and Excluding $b$ary MachinType Individual Digit Formulae
Constants with formulae of the form treated by D.~Bailey,
P.~Borwein, and S.~Plouffe (\emph{BBP formulae} to a given base $b$) have
interesting computational properties, such as allowing single
digits in their base $b$ expansion to be independently computed,
and there are hints that they
should be \emph{normal} numbers, {\em i.e.,} that their base $b$ digits
are randomly distributed. We study a formally limited subset of BBP
formulae, which we call \emph{Machintype BBP formulae}, for which it
is relatively easy to determine whether or not a given constant
$\kappa$ has a Machintype BBP formula. In particular, given $b \in
\mathbb{N}$, $b>2$, $b$ not a proper power, a $b$ary Machintype
BBP arctangent formula for $\kappa$ is a formula of the form $\kappa
= \sum_{m} a_m \arctan(b^{m})$, $a_m \in \mathbb{Q}$, while when
$b=2$, we also allow terms of the form $a_m \arctan(1/(12^m))$. Of
particular interest, we show that $\pi$ has no Machintype BBP
arctangent formula when $b \neq 2$. To the best of our knowledge,
when there is no Machintype BBP formula for a constant then no BBP
formula of any form is known for that constant.
Keywords:BBP formulae, Machintype formulae, arctangents,, logarithms, normality, Mersenne primes, Bang's theorem,, Zsigmondy's theorem, primitive prime factors, $p$adic analysis Categories:11Y99, 11A51, 11Y50, 11K36, 33B10 

14. CJM 2001 (vol 53 pp. 944)
 Ludwig, J.; MolitorBraun, C.

ReprÃ©sentations irrÃ©ductibles bornÃ©es des groupes de Lie exponentiels
Let $G$ be a solvable exponential Lie group. We characterize all the
continuous topologically irreducible bounded representations $(T,
\calU)$ of $G$ on a Banach space $\calU$ by giving a $G$orbit in
$\frn^*$ ($\frn$ being the nilradical of $\frg$), a topologically
irreducible representation of $L^1(\RR^n, \o)$, for a certain weight
$\o$ and a certain $n \in \NN$, and a topologically simple extension
norm. If $G$ is not symmetric, \ie, if the weight $\o$ is
exponential, we get a new type of representations which are
fundamentally different from the induced representations.
Soit $G$ un groupe de Lie r\'esoluble exponentiel. Nous
caract\'erisons toutes les repr\'esentations $(T, \calU)$ continues
born\'ees topologiquement irr\'eductibles de $G$ dans un espace de
Banach $\calU$ \`a l'aide d'une $G$orbite dans $\frn^*$ ($\frn$
\'etant le radical nilpotent de $\frg$), d'une repr\'esentation
topologiquement irr\'eductible de $L^1(\RR^n, \o)$, pour un certain
poids $\o$ et un certain $n \in \NN$, d'une norme d'extension
topologiquement simple. Si $G$ n'est pas sym\'etrique, c. \`a d. si
le poids $\o$ est exponentiel, nous obtenons un nouveau type de
repr\'esentations qui sont fondamentalement diff\'erentes des
repr\'esentations induites.
Keywords:groupe de Lie rÃ©soluble exponentiel, reprÃ©sentation bornÃ©e topologiquement irrÃ©ductible, orbite, norme d'extension, sousespace invariant, idÃ©al premier, idÃ©al primitif Category:43A20 

15. CJM 2000 (vol 52 pp. 897)
 Christiansen, T. J.; Joshi, M. S.

Higher Order Scattering on Asymptotically Euclidean Manifolds
We develop a scattering theory for perturbations of powers of the
Laplacian on asymptotically Euclidean manifolds. The (absolute)
scattering matrix is shown to be a Fourier integral operator
associated to the geodesic flow at time $\pi$ on the boundary.
Furthermore, it is shown that on $\Real^n$ the asymptotics of certain
shortrange perturbations of $\Delta^k$ can be recovered from the
scattering matrix at a finite number of energies.
Keywords:scattering theory, conormal, Lagrangian Category:58G15 

16. CJM 1999 (vol 51 pp. 26)
 Fabian, Marián; Mordukhovich, Boris S.

Separable Reduction and Supporting Properties of FrÃ©chetLike Normals in Banach Spaces
We develop a method of separable reduction for Fr\'{e}chetlike
normals and $\epsilon$normals to arbitrary sets in general Banach
spaces. This method allows us to reduce certain problems involving
such normals in nonseparable spaces to the separable case. It is
particularly helpful in Asplund spaces where every separable subspace
admits a Fr\'{e}chet smooth renorm. As an applicaton of the separable
reduction method in Asplund spaces, we provide a new direct proof of a
nonconvex extension of the celebrated BishopPhelps density theorem.
Moreover, in this way we establish new characterizations of Asplund
spaces in terms of $\epsilon$normals.
Keywords:nonsmooth analysis, Banach spaces, separable reduction, FrÃ©chetlike normals and subdifferentials, supporting properties, Asplund spaces Categories:49J52, 58C20, 46B20 
