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1. CJM 2012 (vol 66 pp. 102)
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 
2. CJM 2010 (vol 63 pp. 123)
Strong and Extremely Strong Ditkin sets for the Banach Algebras $A_p^r(G)=A_p\cap L^r(G)$
Let $A_p(G)$ be the FigaTalamanca,
Herz Banach Algebra on $G$; thus $A_2(G)$
is the Fourier algebra. Strong Ditkin (SD) and
Extremely Strong Ditkin (ESD) sets for the Banach algebras
$A_p^r(G)$ are investigated for abelian and nonabelian
locally compact groups $G$. It is shown that SD and ESD sets
for $A_p(G)$ remain SD and ESD sets for $A_p^r(G)$,
with strict inclusion for ESD sets. The case for the strict
inclusion of SD sets is left open.
A result on the weak sequential completeness of $A_2(F)$
for ESD sets $F$ is proved and used to show that Varopoulos,
Helson, and Sidon sets are not ESD sets for $A_2(G)$, yet they
are such for $A_2^r(G)$ for discrete groups $G$, for
any $1\le r\le 2$.
A result is given on the equivalence of the sequential and the net
definitions of SD or ESD sets for $\sigma$compact groups.
The above results are new even if $G$ is abelian.
Keywords:Fourier algebra, FigaTalamancaHerz algebra, locally compact group, Ditkin sets, Helson sets, Sidon sets, weak sequential completeness Categories:43A15, 43A10, 46J10, 43A45 
3. CJM 2002 (vol 54 pp. 1280)
Besov Spaces and Hausdorff Dimension For Some CarnotCarathÃ©odory Metric Spaces We regard a system of left invariant vector fields $\mathcal{X}=\{X_1,\dots,X_k\}$
satisfying the H\"ormander condition and the related CarnotCarath\'eodory metric on a
unimodular Lie group $G$. We define Besov spaces corresponding to the subLaplacian
$\Delta=\sum X_i^2$ both with positive and negative smoothness. The atomic
decomposition of the spaces is given. In consequence we get the distributional
characterization of the Hausdorff dimension of Borel subsets with the Haar measure
zero.
Keywords:Besov spaces, subelliptic operators, CarnotCarathÃ©odory metric, Hausdorff dimension Categories:46E35, 43A15, 28A78 
4. CJM 2002 (vol 54 pp. 303)
Convergence Factors and Compactness in Weighted Convolution Algebras We study convergence in weighted convolution algebras $L^1(\omega)$ on
$R^+$, with the weights chosen such that the corresponding weighted
space $M(\omega)$ of measures is also a Banach algebra and is the dual
space of a natural related space of continuous functions. We
determine convergence factor $\eta$ for which
weak$^\ast$convergence of $\{\lambda_n\}$ to $\lambda$ in $M(\omega)$
implies norm convergence of $\lambda_n \ast f$ to $\lambda \ast f$ in
$L^1 (\omega\eta)$. We find necessary and sufficent conditions which
depend on $\omega$ and $f$ and also find necessary and sufficent
conditions for $\eta$ to be a convergence factor for all $L^1(\omega)$
and all $f$ in $L^1(\omega)$. We also give some applications to the
structure of weighted convolution algebras. As a preliminary result
we observe that $\eta$ is a convergence factor for $\omega$ and $f$ if
and only if convolution by $f$ is a compact operator from $M(\omega)$
(or $L^1(\omega)$) to $L^1 (\omega\eta)$.
Categories:43A10, 43A15, 46J45, 46J99 
5. CJM 1998 (vol 50 pp. 897)
Fourier multipliers for local hardy spaces on ChÃ©bliTrimÃ¨che hypergroups In this paper we consider Fourier multipliers on local
Hardy spaces $\qin$ $(0
