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Subspaces of de~Branges Spaces Generated by Majorants |
Canad. J. Math. 61(2009), 503-517
Published:2009-06-01
Printed: Jun 2009
Printed: Jun 2009
- Anton Baranov
- Harald Woracek
Abstract
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 |
| MSC Classifications: |
46E20 - Hilbert spaces of continuous, differentiable or analytic functions 30D15 - Special classes of entire functions and growth estimates 46E22 - Hilbert spaces with reproducing kernels (= [proper] functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) [See also 47B32] |