Subspaces of de Branges Spaces Generated by Majorants

Baranov, Anton ; Woracek, Harald

Canadian journal of mathematics, Tome 61 (2009) no. 3, pp. 503-517

Résumé

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.

Détail

DOI : 10.4153/CJM-2009-026-2

Mots-clés : 46E20, 30D15, 46E22, Branges subspace, majorant, Beurling-Malliavin Theorem

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