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# Subspaces of de~Branges Spaces Generated by Majorants

Published:2009-06-01
Printed: Jun 2009
• Anton Baranov
• Harald Woracek
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## 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]