Stability of shifts, interpolation, and spectrum of atomic measures

IF 1.2 2区数学 Q1 MATHEMATICS

Journal of the London Mathematical Society-Second Series Pub Date : 2025-08-26 DOI:10.1112/jlms.70267

Alexander Ulanovskii, Ilya Zlotnikov

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引用次数: 0

Abstract

We ask which functions $G$ and separated sets $Γ$ have the property that the $Γ$ -shifts of $G$ form an unconditional basis in the $L^{p} (R)$ -closure of their span for every $p \in [1, \infty]$ . The main result establishes the equivalence of this property to each of the two seemingly unrelated conditions: $Γ$ is a set of interpolation for certain Paley–Wiener spaces and the nonexistence of certain measures with given support and spectrum. As a consequence, we answer the question for wide classes of functions $G$ and sets $Γ$ . In particular, we show the connection between the property and the nonexistence of certain crystalline measures.

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位移的稳定性，插值，和光谱的原子措施

我们问哪些函数G $\mathcal {G}$和分离集Γ $\Gamma$具有这样的性质：G $\mathcal {G}$的Γ $\Gamma$ -移位在L p (R) $L^p({\mathbb {R}})$ -它们张成的闭包对于每一个p∈[1，[∞]$p\in [1,\infty]$。主要结果建立了这一性质对两个看似不相关的条件中的每一个的等价性：Γ $\Gamma$是特定的Paley-Wiener空间的一组插值和给定支持和谱的某些测度的不存在性。因此，我们回答了广义类函数G $\mathcal {G}$和集合Γ $\Gamma$的问题。我们特别指出了这种性质与某些结晶测度的不存在之间的联系。

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来源期刊

Journal of the London Mathematical Society-Second Series 数学-数学

CiteScore

1.90

自引率

0.00%

发文量

186

审稿时长

6-12 weeks

期刊介绍： The Journal of the London Mathematical Society has been publishing leading research in a broad range of mathematical subject areas since 1926. The Journal welcomes papers on subjects of general interest that represent a significant advance in mathematical knowledge, as well as submissions that are deemed to stimulate new interest and research activity.