1. CJM 2017 (vol 69 pp. 1312)
 Fricain, Emmanuel; Rupam, Rishika

On Asymptotically Orthonormal Sequences
An asymptotically orthonormal sequence is a sequence which is
"nearly" orthonormal in the sense that it satisfies the Parseval
equality up to two constants close to one. In this paper, we
explore such sequences formed by normalized reproducing kernels
for model spaces and de BrangesRovnyak spaces.
Keywords:function space, de BrangesRovnyak and model space, reproducing kernel, asymptotically orthonormal sequence Categories:30J05, 30H10, 46E22 

2. CJM 2016 (vol 69 pp. 54)
 Hartz, Michael

On the Isomorphism Problem for Multiplier Algebras of NevanlinnaPick Spaces
We continue the investigation of the isomorphism problem for
multiplier algebras of reproducing kernel
Hilbert spaces with the complete NevanlinnaPick property.
In contrast to previous work in this area,
we do not study these spaces by identifying them with restrictions
of a universal space, namely the DruryArveson space.
Instead, we work directly with the Hilbert spaces and their
reproducing kernels. In particular,
we show that two multiplier algebras of NevanlinnaPick spaces
on the same set are equal if and only if the Hilbert
spaces are equal. Most of the article is devoted to the study
of a special class of
complete NevanlinnaPick spaces on homogeneous varieties. We
provide a complete
answer to the question of when two multiplier algebras of spaces
of this type
are algebraically or isometrically isomorphic. This generalizes
results of Davidson, Ramsey, Shalit,
and the author.
Keywords:nonselfadjoint operator algebras, reproducing kernel Hilbert spaces, multiplier algebra, NevanlinnaPick kernels, isomorphism problem Categories:47L30, 46E22, 47A13 

3. CJM 2009 (vol 61 pp. 503)
 Baranov, Anton; Woracek, Harald

Subspaces of de~Branges Spaces Generated by Majorants
For a given de~Branges space $\mc H(E)$ we investigate
de~Branges subspaces defined in terms of majorants
on the real axis. If $\omega$ is a nonnegative function on $\mathbb R$,
we consider the subspace
\[
\mc R_\omega(E)=\clos_{\mc H(E)} \big\{F\in\mc H(E):
\text{ there exists } C>0:
E^{1} F\leq C\omega \mbox{ on }{\mathbb R}\big\}
.
\]
We show that $\mc R_\omega(E)$ is a de~Branges subspace and
describe all subspaces of this form. Moreover,
we give a criterion for the existence of positive minimal majorants.
Keywords:de~Branges subspace, majorant, BeurlingMalliavin Theorem Categories:46E20, 30D15, 46E22 

4. 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 
