The Beurling--Malliavin Multiplier Theorem and its analogs for the de Branges spaces

2013/09/27 by Yurii Belov, Belov, Yurii, V. P. Havin +1
Mathematics · #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.1309.7130

openalex publication_date 2013/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let ω be a non-negative function on ℝ. We are looking for a non-zero f from a given space of entire functions X satisfying (a) |f|≤ ω or (b) |f|\asympω. The classical Beurling--Malliavin Multiplier Theorem corresponds to (a) and the classical Paley--Wiener space as X. We survey recent results for the case when X is a de Branges space \he. Numerous answers mainly depend on the behaviour of the phase function of the generating function E.

Related

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• A remark on the Beurling-Malliavin theorem in several variables
• Examples of de Branges-Rovnyak spaces generated by nonextreme functions
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