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Search: MSC category 46E22 ( Hilbert spaces with reproducing kernels (= [proper] functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) [See also 47B32] )

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1. 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, Beurling-Malliavin Theorem
Categories:46E20, 30D15, 46E22

2. 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

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