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arXiv · 1309.7130

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

Yurii Belov·Victor Havin
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Abstract

Let $ω$ be a non-negative function on $\mathbb{R}$. We are looking for a non-zero $f$ from a given space of entire functions $X$ satisfying $$(a) \quad|f|\leq ω\text{\quad or\quad(b)}\quad |f|\asympω.$$ 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 $E$.

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Yurii Belov, Victor Havin. 2013-09-27. The Beurling--Malliavin Multiplier Theorem and its analogs for the de Branges spaces. https://arxiv.org/abs/1309.7130

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