Spectral synthesis in Hilbert spaces of entire functions
type: Item
instance of: scholarly article
title: Spectral synthesis in Hilbert spaces of entire functions
zbMATH Open document ID: 1441.30037
DOI: 10.4171/176-1/8
author: A. D. Baranov
author: Yurii Belov
publication date: 2018-11-14T00:00:00Z
review text: Summary: We give a survey of recent advances in the theory of spaces of entire functions related to the notion of spectral synthesis. In particular, we discuss a solution of a longstanding problem about spectral synthesis for systems of exponentials in \(L^2(-\pi, \pi)\) as well as its generalization to de Branges spaces of entire functions. In the de Branges space setting the problem can be related (via a functional model) to spectral theory of rank one perturbations of compact selfadjoint operators; this leads to unexpected examples of rank one perturbations which do not admit spectral synthesis. Related problems for Fock-type spaces are also considered. For the entire collection see [Zbl 1396.00017].
Mathematics Subject Classification ID: 30D15
Mathematics Subject Classification ID: 30H99
zbMATH DE Number: 6979385
zbMATH Keywords: entire functions
zbMATH Keywords: systems of exponentials
zbMATH Keywords: de Branges spaces
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4171/176-1/8
OpenAlex ID: W4252743041
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description: scientific article; zbMATH DE number 6979385