1. CJM 2012 (vol 66 pp. 700)
 He, Jianxun; Xiao, Jinsen

Inversion of the Radon Transform on the Free Nilpotent Lie Group of Step Two
Let $F_{2n,2}$ be the free nilpotent Lie group of step two on $2n$
generators, and let $\mathbf P$ denote the affine automorphism group
of $F_{2n,2}$. In this article the theory of continuous wavelet
transform on $F_{2n,2}$ associated with $\mathbf P$ is developed,
and then a type of radial wavelets is constructed. Secondly, the
Radon transform on $F_{2n,2}$ is studied and two equivalent
characterizations of the range for Radon transform are given.
Several kinds of inversion Radon transform formulae
are established. One is obtained from the Euclidean Fourier transform, the others are from group Fourier transform. By using wavelet transform we deduce an inversion formula of the Radon
transform, which
does not require the smoothness of
functions if the wavelet satisfies the differentiability property.
Specially, if $n=1$, $F_{2,2}$ is the $3$dimensional Heisenberg group $H^1$, the
inversion formula of the Radon transform is valid which is
associated with the subLaplacian on $F_{2,2}$. This result cannot
be extended to the case $n\geq 2$.
Keywords:Radon transform, wavelet transform, free nilpotent Lie group, unitary representation, inversion formula, subLaplacian Categories:43A85, 44A12, 52A38 

2. CJM 2005 (vol 57 pp. 598)
 Kornelson, Keri A.

Local Solvability of Laplacian Difference Operators Arising from the Discrete Heisenberg Group
Differential operators $D_x$, $D_y$, and $D_z$ are formed using the
action of the $3$dimensional discrete Heisenberg group $G$ on a set
$S$, and the operators will act on functions on $S$. The Laplacian
operator $L=D_x^2 + D_y^2 + D_z^2$ is a difference operator with
variable differences which can be associated to a unitary
representation of $G$ on the Hilbert space $L^2(S)$. Using techniques
from harmonic analysis and representation theory, we show that the
Laplacian operator is locally solvable.
Keywords:discrete Heisenberg group,, unitary representation,, local solvability,, difference operator Categories:43A85, 22D10, 39A70 

3. CJM 2003 (vol 55 pp. 1134)
 Casarino, Valentina

Norms of Complex Harmonic Projection Operators
In this paper we estimate the $(L^pL^2)$norm of the complex
harmonic projectors $\pi_{\ell\ell'}$, $1\le p\le 2$, uniformly
with respect to the indexes $\ell,\ell'$. We provide sharp
estimates both for the projectors $\pi_{\ell\ell'}$, when
$\ell,\ell'$ belong to a proper angular sector in $\mathbb{N}
\times \mathbb{N}$, and for the projectors $\pi_{\ell 0}$ and
$\pi_{0 \ell}$. The proof is based on an extension of a complex
interpolation argument by C.~Sogge. In the appendix, we prove in a
direct way the uniform boundedness of a particular zonal kernel in
the $L^1$ norm on the unit sphere of $\mathbb{R}^{2n}$.
Categories:43A85, 33C55, 42B15 

4. CJM 1999 (vol 51 pp. 952)
 Deitmar, Anton; Hoffmann, Werner

On Limit Multiplicities for Spaces of Automorphic Forms
Let $\Gamma$ be a rankone arithmetic subgroup of a
semisimple Lie group~$G$. For fixed $K$Type, the spectral
side of the Selberg trace formula defines a distribution
on the space of infinitesimal characters of~$G$, whose
discrete part encodes the dimensions of the spaces of
squareintegrable $\Gamma$automorphic forms. It is shown
that this distribution converges to the Plancherel measure
of $G$ when $\Ga$ shrinks to the trivial group in a certain
restricted way. The analogous assertion for cocompact
lattices $\Gamma$ follows from results of DeGeorgeWallach
and Delorme.
Keywords:limit multiplicities, automorphic forms, noncompact quotients, Selberg trace formula, functional calculus Categories:11F72, 22E30, 22E40, 43A85, 58G25 

5. CJM 1998 (vol 50 pp. 1090)
6. CJM 1997 (vol 49 pp. 1224)
 Ørsted, Bent; Zhang, Genkai

Tensor products of analytic continuations of holomorphic discrete series
We give the irreducible decomposition
of the tensor product of an analytic continuation of
the holomorphic discrete
series of $\SU(2, 2)$ with its conjugate.
Keywords:Holomorphic discrete series, tensor product, spherical function, ClebschGordan coefficient, Plancherel theorem Categories:22E45, 43A85, 32M15, 33A65 

7. CJM 1997 (vol 49 pp. 883)