1. CJM 2016 (vol 68 pp. 841)
 Gupta, Sanjiv Kumar; Hare, Kathryn

Characterizing the Absolute Continuity of the Convolution of Orbital Measures in a Classical Lie Algebra
Let $\mathfrak{g}$ be a compact, simple Lie algebra of dimension
$d$. It is
a classical result that the convolution of any $d$ nontrivial,
$G$invariant,
orbital measures is absolutely continuous with respect to
Lebesgue measure on $\mathfrak{g}$ and the sum of any $d$ nontrivial
orbits
has nonempty interior. The number $d$ was later reduced to the
rank of the
Lie algebra (or rank $+1$ in the case of type $A_{n}$). More
recently, the
minimal integer $k=k(X)$ such that the $k$fold convolution of
the orbital
measure supported on the orbit generated by $X$ is an absolutely
continuous
measure was calculated for each $X\in \mathfrak{g}$.
In this paper $\mathfrak{g}$ is any of the classical, compact,
simple Lie
algebras. We characterize the tuples $(X_{1},\dots,X_{L})$, with
$X_{i}\in
\mathfrak{g},$ which have the property that the convolution of
the $L$orbital
measures supported on the orbits generated by the $X_{i}$ is
absolutely continuous and, equivalently, the sum of their orbits
has
nonempty interior. The characterization depends on the Lie type
of
$\mathfrak{g}$ and the structure of the annihilating roots of
the $X_{i}$.
Such a characterization was previously known only for type $A_{n}$.
Keywords:compact Lie algebra, orbital measure, absolutely continuous measure Categories:43A80, 17B45, 58C35 

2. CJM 2016 (vol 68 pp. 816)
 Guo, Xiaoli; Hu, Guoen

On the Commutators of Singular Integral Operators with Rough Convolution Kernels
Let $T_{\Omega}$ be the singular integral operator with kernel
$\frac{\Omega(x)}{x^n}$, where $\Omega$ is homogeneous of degree
zero, has mean value zero and belongs to $L^q(S^{n1})$ for
some
$q\in (1,\,\infty]$. In this paper, the authors establish the
compactness on weighted $L^p$ spaces, and the Morrey spaces,
for the commutator generated by $\operatorname{CMO}(\mathbb{R}^n)$ function
and $T_{\Omega}$. The associated maximal operator and the discrete
maximal operator are also considered.
Keywords:commutator, singular integral operator, compact operator, completely continuous operator, maximal operator, Morrey space Categories:42B20, 47B07 

3. CJM 2015 (vol 67 pp. 1091)
 Mine, Kotaro; Yamashita, Atsushi

Metric Compactifications and Coarse Structures
Let $\mathbf{TB}$ be the category of totally bounded, locally
compact metric spaces
with the $C_0$ coarse structures. We show that if $X$ and $Y$
are in $\mathbf{TB}$ then $X$ and $Y$ are coarsely equivalent
if and only if their Higson coronas are homeomorphic. In fact,
the Higson corona functor gives an equivalence of categories
$\mathbf{TB}\to\mathbf{K}$, where $\mathbf{K}$ is the category
of compact metrizable spaces. We use this fact to show that the
continuously controlled coarse structure on a locally compact
space $X$ induced by some metrizable compactification $\tilde{X}$
is determined only by the topology of the remainder $\tilde{X}\setminus
X$.
Keywords:coarse geometry, Higson corona, continuously controlled coarse structure, uniform continuity, boundary at infinity Categories:18B30, 51F99, 53C23, 54C20 

4. CJM 2015 (vol 67 pp. 481)
 an Huef, Astrid; Archbold, Robert John

The C*algebras of Compact Transformation Groups
We investigate the representation theory of the
crossedproduct $C^*$algebra associated to a compact group $G$
acting on a locally compact space $X$ when the stability subgroups
vary discontinuously.
Our main result applies when $G$ has a principal stability subgroup or
$X$ is locally of finite $G$orbit type. Then the upper multiplicity
of the representation of the crossed product induced from an
irreducible representation $V$ of a stability subgroup is obtained by
restricting $V$ to a certain closed subgroup of the stability subgroup
and taking the maximum of the multiplicities of the irreducible
summands occurring in the restriction of $V$. As a corollary we obtain
that when the trivial subgroup is a principal stability subgroup, the
crossed product is a Fell algebra if and only if every stability
subgroup is abelian. A second corollary is that the $C^*$algebra of
the motion group $\mathbb{R}^n\rtimes \operatorname{SO}(n)$ is a Fell algebra. This uses
the classical branching theorem for the special orthogonal group
$\operatorname{SO}(n)$ with respect to $\operatorname{SO}(n1)$. Since proper transformation
groups are locally induced from the actions of compact groups, we
describe how some of our results can be extended to transformation
groups that are locally proper.
Keywords:compact transformation group, proper action, spectrum of a C*algebra, multiplicity of a representation, crossedproduct C*algebra, continuoustrace C*algebra, Fell algebra Categories:46L05, 46L55 

5. CJM 2014 (vol 67 pp. 330)
 Bernardes, Nilson C.; Vermersch, Rômulo M.

Hyperspace Dynamics of Generic Maps of the Cantor Space
We study the hyperspace dynamics induced from generic continuous maps
and from generic homeomorphisms of the Cantor space, with emphasis on the
notions of LiYorke chaos, distributional chaos, topological entropy,
chain continuity, shadowing and recurrence.
Keywords:cantor space, continuous maps, homeomorphisms, hyperspace, dynamics Categories:37B99, 54H20, 54E52 

6. CJM 2013 (vol 65 pp. 1005)
 Forrest, Brian; Miao, Tianxuan

Uniformly Continuous Functionals and MWeakly Amenable Groups
Let $G$ be a locally compact group. Let $A_{M}(G)$ ($A_{0}(G)$)denote
the closure of $A(G)$, the Fourier algebra of $G$ in the space of
bounded (completely bounded) multipliers of $A(G)$.
We call a locally compact group Mweakly amenable if
$A_M(G)$
has a
bounded approximate identity. We will show that when $G$ is Mweakly
amenable, the algebras $A_{M}(G)$ and $A_{0}(G)$ have
properties that are characteristic of the Fourier algebra of an
amenable group. Along the way we show that the sets of tolopolically
invariant means associated with these algebras have the same
cardinality as those of the Fourier algebra.
Keywords:Fourier algebra, multipliers, weakly amenable, uniformly continuous functionals Categories:43A07, 43A22, 46J10, 47L25 

7. CJM 2011 (vol 64 pp. 755)
 Brown, Lawrence G.; Lee, Hyun Ho

Homotopy Classification of Projections in the Corona Algebra of a Nonsimple $C^*$algebra
We study projections in the corona algebra of $C(X)\otimes K$, where K
is the $C^*$algebra of compact operators on a separable infinite
dimensional Hilbert space and $X=[0,1],[0,\infty),(\infty,\infty)$,
or $[0,1]/\{ 0,1 \}$. Using BDF's essential codimension, we determine
conditions for a projection in the corona algebra to be liftable to a
projection in the multiplier algebra. We also determine the
conditions for two projections to be equal in $K_0$, Murrayvon
Neumann equivalent, unitarily equivalent, or homotopic. In light of
these characterizations, we construct examples showing that the
equivalence notions above are all distinct.
Keywords:essential codimension, continuous field of Hilbert spaces, Corona algebra Categories:46L05, 46L80 

8. CJM 2011 (vol 63 pp. 1188)
 Śliwa, Wiesław; Ziemkowska, Agnieszka

On Complemented Subspaces of NonArchimedean Power Series Spaces
The nonarchimedean power series spaces, $A_1(a)$ and $A_\infty(b)$, are the
best known and most important examples of nonarchimedean nuclear FrÃ©chet spaces.
We prove that the range of every continuous linear map from $A_p(a)$ to $A_q(b)$
has a Schauder basis if either $p=1$ or $p=\infty$ and the set $M_{b,a}$ of all
bounded limit points of the double sequence
$(b_i/a_j)_{i,j\in\mathbb{N}}$ is bounded. It
follows that every complemented subspace of a power series space $A_p(a)$ has a
Schauder basis if either $p=1$ or $p=\infty$ and the set $M_{a,a}$ is bounded.
Keywords:nonarchimedean KÃ¶the space, range of a continuous linear map, Schauder basis Categories:46S10, 47S10, 46A35 

9. CJM 2011 (vol 63 pp. 500)
 Dadarlat, Marius; Elliott, George A.; Niu, Zhuang

OneParameter Continuous Fields of Kirchberg Algebras. II
Parallel to the first two authors' earlier classification of separable, unita
oneparameter, continuous fields of Kirchberg algebras with torsion free
$\mathrm{K}$groups supported in one dimension, oneparameter, separable, uni
continuous fields of AFalgebras are classified by their ordered
$\mathrm{K}_0$sheaves. EffrosHandelmanShen type theorems are pr separable
unital oneparameter continuous fields of AFalgebras and Kirchberg algebras.
Keywords:continuous fields of C$^*$algebras, $\mathrm{K}_0$presheaves, EffrosHandeen type theorem Category:46L35 

10. CJM 2010 (vol 63 pp. 181)
 Ismail, Mourad E. H.; Obermaier, Josef

Characterizations of Continuous and Discrete $q$Ultraspherical Polynomials
We characterize the continuous $q$ultraspherical polynomials in
terms of the special form of the coefficients in the expansion
$\mathcal{D}_q P_n(x)$ in the basis $\{P_n(x)\}$, $\mathcal{D}_q$
being the AskeyWilson divided difference operator. The polynomials
are assumed to be symmetric, and the connection coefficients
are multiples of the reciprocal of the square of the $L^2$ norm of
the polynomials. A similar characterization is given for the discrete
$q$ultraspherical polynomials. A new proof of the evaluation of
the connection coefficients for big $q$Jacobi polynomials is given.
Keywords:continuous $q$ultraspherical polynomials, big $q$Jacobi polynomials, discrete $q$ultra\spherical polynomials, AskeyWilson operator, $q$difference operator, recursion coefficients Categories:33D45, 42C05 

11. CJM 2007 (vol 59 pp. 1135)
 Björn, Anders; Björn, Jana; Shanmugalingam, Nageswari

Sobolev Extensions of HÃ¶lder Continuous and Characteristic Functions on Metric Spaces
We study when characteristic and H\"older continuous functions
are traces of Sobolev functions on doubling metric measure spaces.
We provide analytic and geometric conditions sufficient for extending
characteristic and H\"older continuous functions into globally defined
Sobolev functions.
Keywords:characteristic function, Newtonian function, metric space, resolutivity, HÃ¶lder continuous, Perron solution, $p$harmonic, Sobolev extension, Whitney covering Categories:46E35, 31C45 

12. CJM 2007 (vol 59 pp. 3)
 Biller, Harald

Holomorphic Generation of Continuous Inverse Algebras
We study complex commutative Banach algebras
(and, more generally, continuous
inverse algebras) in which the holomorphic functions of a fixed $n$tuple
of elements are dense. In particular, we characterize the compact subsets
of~$\C^n$ which appear as joint spectra of such $n$tuples. The
characterization is compared with several established notions of holomorphic
convexity by means of approximation
conditions.
Keywords:holomorphic functional calculus, commutative continuous inverse algebra, holomorphic convexity, Stein compacta, meromorphic convexity, holomorphic approximation Categories:46H30, 32A38, 32E30, 41A20, 46J15 

13. CJM 2005 (vol 57 pp. 471)
 Ciesielski, Krzysztof; Pawlikowski, Janusz

Small Coverings with Smooth Functions under the Covering Property Axiom
In the paper we formulate a Covering Property Axiom, \psmP,
which holds in the iterated perfect set model,
and show that it implies the following facts,
of which (a) and (b) are the generalizations
of results of J. Stepr\={a}ns.
\begin{compactenum}[\rm(a)~~]
\item There exists a family $\F$ of less than continuum many $\C^1$
functions from $\real$ to $\real$ such that $\real^2$ is covered
by functions from $\F$, in the sense that for every $\la
x,y\ra\in\real^2$ there exists an $f\in\F$ such that either
$f(x)=y$ or $f(y)=x$.
\item For every Borel function $f\colon\real\to\real$ there exists a
family $\F$ of less than continuum many ``$\C^1$'' functions ({\em
i.e.,} differentiable functions with continuous derivatives, where
derivative can be infinite) whose graphs cover the graph of $f$.
\item For every $n>0$ and
a $D^n$ function $f\colon\real\to\real$ there exists
a family $\F$ of less than continuum many $\C^n$ functions
whose graphs cover the graph of $f$.
\end{compactenum}
We also provide the examples showing that in the above properties
the smoothness conditions are the best possible. Parts (b), (c),
and the examples are closely related to work of
A. Olevski\v{\i}.
Keywords:continuous, smooth, covering Categories:26A24, 03E35 

14. CJM 2002 (vol 54 pp. 709)
 Ismail, Mourad E. H.; Stanton, Dennis

$q$Integral and Moment Representations for $q$Orthogonal Polynomials
We develop a method for deriving integral representations of certain
orthogonal polynomials as moments. These moment representations are
applied to find linear and multilinear generating functions for
$q$orthogonal polynomials. As a byproduct we establish new
transformation formulas for combinations of basic hypergeometric
functions, including a new representation of the $q$exponential
function $\mathcal{E}_q$.
Keywords:$q$integral, $q$orthogonal polynomials, associated polynomials, $q$difference equations, generating functions, AlSalamChihara polynomials, continuous $q$ultraspherical polynomials Categories:33D45, 33D20, 33C45, 30E05 

15. CJM 1997 (vol 49 pp. 1089)
 Burke, Maxim R.; Ciesielski, Krzysztof

Sets on which measurable functions are determined by their range
We study sets on which measurable realvalued functions on a
measurable space with negligibles are determined by their range.
Keywords:measurable function, measurable space with negligibles, continuous image, set of range uniqueness (SRU) Categories:28A20, 28A05, 54C05, 26A30, 03E35, 03E50 

16. CJM 1997 (vol 49 pp. 520)
 Ismail, Mourad E. H.; Stanton, Dennis

Classical orthogonal polynomials as moments
We show that the Meixner, Pollaczek, MeixnerPollaczek, the continuous
$q$ultraspherical polynomials and AlSalamChihara polynomials, in
certain normalization, are moments of probability measures. We use
this fact to derive bilinear and multilinear generating functions for
some of these polynomials. We also comment on the corresponding formulas
for the Charlier, Hermite and Laguerre polynomials.
Keywords:Classical orthogonal polynomials, \ACP, continuous, $q$ultraspherical polynomials, generating functions, multilinear, generating functions, transformation formulas, umbral calculus Categories:33D45, 33D20, 33C45, 30E05 
