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Subspaces of de Branges Spaces Generated by Majorants

Published online by Cambridge University Press:  20 November 2018

Anton Baranov  and
Harald Woracek
Anton Baranov
Affiliation:
Department of Mathematics and Mechanics, Saint Petersburg State University, 28, Universitetski pr., 198504 St. Petersburg, Russia, [email protected]
Harald Woracek
Affiliation:
Institute for Analysis and ScientificComputing, ViennaUniversity of Technology, WiednerHauptstr. 8-10/101, 1040 Vienna, Austria, [email protected]
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Abstract

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For a given de Branges space $\mathcal{H}(E)$ 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

$${{\mathcal{R}}_{\omega }}(E)=\text{Clo}{{\text{s}}_{\mathcal{H}(E)}}\{F\in \mathcal{H}(E):\text{there exists }C>0:|{{E}^{-1}}F|\le C\omega \,on\,\mathbb{R}\}.$$

We show that ${{\mathcal{R}}_{\omega }}(E)$ 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

46E2030D1546E22Branges subspacemajorantBeurling-Malliavin Theorem
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 61 , Issue 3 , 01 June 2009 , pp. 503 - 517
Copyright
Copyright © Canadian Mathematical Society 2009

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