© Springer Basel 2015. All rights are reserved. Let ω be a non-negative function on R. Is it true that there exists a non-zero f from a given space of entire functions X satisfying (a) |f|≤ω or (b) |f| = ω? The classical Beurling-MalliavinMultiplier Theorem corresponds to (a) and the classical Paley-Wiener space as X. This is a survey of recent results for the case when X is a de Branges space H.E/. Numerous answers mainly depend on the behavior of the phase function of the generating function E. For example, if argE is regular, then for any even positive ! non-increasing on [0;∞) with log! Ε L1((1 + x2/-1dx) there exists a non-zero f Ε H(E) such that |f| ≤ |E|ω. This is no longer true for the irregular case. The Toeplitz kernel approach to these problems is discussed. This method was recently developed by N. Makarov and A. Poltoratski.
Язык оригиналаанглийский
Название основной публикацииOperator Theory
ИздательSpringer Nature
Страницы581-607
ISBN (печатное издание)9783034806671; 9783034806664
DOI
СостояниеОпубликовано - 2015

ID: 3988614