51. CJM 1998 (vol 50 pp. 658)
 Symesak, Frédéric

Hankel operators on pseudoconvex domains of finite type in ${\Bbb C}^2$
The aim of this paper is to study small Hankel operators $h$ on the
Hardy space or on weighted Bergman spaces, where $\Omega$ is a
finite type domain in ${\Bbbvii C}^2$ or a strictly pseudoconvex
domain in ${\Bbbvii C}^n$. We give a sufficient condition on the
symbol $f$ so that $h$ belongs to the Schatten class ${\cal S}_p$,
$1\le p<+\infty$.
Categories:32A37, 47B35, 47B10, 46E22 

52. CJM 1998 (vol 50 pp. 99)
 Izuchi, Keiji; Matsugu, Yasuo

$A_\phi$invariant subspaces on the torus
Generalizing the notion of invariant subspaces on
the 2dimensional torus $T^2$, we study the structure
of $A_\phi$invariant subspaces of $L^2(T^2)$. A
complete description is given of $A_\phi$invariant
subspaces that satisfy conditions similar to those
studied by Mandrekar, Nakazi, and Takahashi.
Categories:32A35, 47A15 

53. CJM 1997 (vol 49 pp. 1299)
 Tie, Jingzhi

The explicit solution of the $\bar\partial$Neumann problem in a nonisotropic Siegel domain
In this paper, we solve the $\dbar$Neumann problem
on $(0,q)$ forms, $0\leq q \leq n$, in the strictly
pseudoconvex nonisotropic Siegel domain:
\[
\cU=\left\{
\begin{array}{clc}
&\bz=(z_1,\ldots,z_n) \in \C^{n},\\
(\bz,z_{n+1}):&&\Im (z_{n+1}) > \sum_{j=1}^{n}a_j z_j^2 \\
&z_{n+1}\in \C;
\end{array}
\right\},
\]
where $a_j> 0$ for $j=1,2,\ldots, n$. The metric we
use is invariant under the action of the Heisenberg
group on the domain. The fundamental solution of the
related differential equation is derived via the
Laguerre calculus. We obtain an explicit formula for
the kernel of the Neumann operator. We also construct
the solution of the corresponding heat equation and
the fundamental solution of the Laplacian operator
on the Heisenberg group.
Categories:32F15, 32F20, 35N15 

54. 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 

55. CJM 1997 (vol 49 pp. 916)
 Brylinski, Ranee

Quantization of the $4$dimensional nilpotent orbit of SL(3,$\mathbb{R}$)
We give a new geometric model for the quantization
of the 4dimensional conical (nilpotent) adjoint orbit
$O_\mathbb{R}$ of SL$(3,\mathbb{R})$. The space of quantization is the space of
holomorphic functions on $\mathbb{C}^2 \{ 0 \}$ which are square integrable
with respect to a signed measure defined by a Meijer $G$function.
We construct the quantization out a nonflat Kaehler structure on
$\mathbb{C}^2  \{ 0 \}$ (the universal cover of $O_\mathbb{R}$ ) with Kaehler potential
$\rho=z^4$.
Categories:81S10, 32C17, 22E70 

56. CJM 1997 (vol 49 pp. 653)