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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 de~Branges subspace, majorant, Beurling-Malliavin Theorem
MSC Classifications: 46E20, 30D15, 46E22 show english descriptions Hilbert spaces of continuous, differentiable or analytic functions
Special classes of entire functions and growth estimates
Hilbert spaces with reproducing kernels (= [proper] functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) [See also 47B32]
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]
 

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