Beurling-Malliavin theory for Toeplitz kernels

关于多变量中的Beurling-Malliavin定理的注记

A remark on the Beurling-Malliavin theorem in several variables

本文通过提升技巧证明多变量中Beurling-Malliavin定理可扩展至径向函数，并简化了Vasilyev的论证并回答了其关于Cartwright版本的问题。

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

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 $E$.

内逼近双倍权重及其在Toeplitz核的Beurling-Malliavin理论中的应用

Inner approximations of doubling weights with applications to Beurling-Malliavin theory in Toeplitz kernels

本文研究了如何用Meromorphic内函数的论证逼近任意递增函数，特别探讨了满足双倍条件的函数的逼近问题，并应用于Toeplitz核零集的密度条件和模型空间的Beurling-Malliavin主量类描述。

Subharmonic addition to the Beurling-Malliavin multiplier theorem

We prove a version of the Beurling-Malliavin multiplier theorem. This version is formulated here in a simplified form. Let $u\not\equiv -\infty$ and $M\not\equiv -\infty$ be a pair of subharmonic functions on the complex plane $\mathbb C$ with positive parts $u^+:=\sup\{u,0\}$ and $M^+$ such that $$ \operatorname{type}[u]:=\limsup_{z\to \infty} \frac{u^+(z)}{|z|}<+\infty, \qquad \operatorname{type}[M]<+\infty, \qquad \int_{-\infty}^{+\infty}\frac{u^+(x)+M^+(x)}{1+x^2}\operatorname{d}x<+\infty. $$ If $\operatorname{type}[u]<a<+\infty$, $0<b<+\infty$, and $\operatorname{type}[M]<c<+\infty$, then…

Beurling广义整数的最佳Malliavin型余项

The optimal Malliavin-type remainder for Beurling generalized integers

本文建立了Beurling广义整数渐近密度逼近公式中Malliavin型余项的最佳阶，通过构造广义数系并利用Riemann素数计数函数与整数计数函数的极值振荡估计，改进并推广了先前工作。

Polya sequences, Toeplitz kernels and gap theorems

A separated sequence $Λ$ on the real line is called a Polya sequence if any entire function of zero exponential type bounded on $Λ$ is constant. In this paper we solve the problem by Polya and Levinson that asks for a description of Polya sets. We also show that the Polya-Levinson problem is equivalent to a version of the so-called Beurling gap problem on Fourier transforms of measures. The solution is obtained via a recently developed approach based on the use of Toeplitz kernels and de Branges spaces of entire functions.