Frame set for shifted sinc-function

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Applied and Computational Harmonic Analysis Pub Date : 2024-03-16 DOI:10.1016/j.acha.2024.101654

Yurii Belov , Andrei V. Semenov

引用次数: 0

Abstract

We prove that frame set $F_{g}$ for imaginary shift of sinc-function $g (t) = \frac{\sin π b (t - i w)}{t - i w}, b, w \in R ∖ {0}$ can be described as $F_{g} = {(α, β) : α β ⩽ 1, β ⩽ | b |}$ .

In addition, we prove that $F_{g} = {(α, β) : α β ⩽ 1}$ for window functions g of the form $\frac{1}{t - i w} (1 - \sum_{k = 1}^{\infty} a_{k} e^{2 π i b_{k} t}),$ such that $\sum_{k ⩾ 1} | a_{k} | e^{2 π | w b_{k} |} < 1$ , $w b_{k} < 0$ .

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移位 sinc 函数的帧集

我们证明，sinc 函数g(t)=sinπb(t-iw)t-iw,b,w∈R∖{0}的虚移帧集 Fg 可描述为 Fg={(α,β):αβ⩽1,β⩽|b|}。此外，我们还证明，Fg={(α,β):αβ⩽1}为窗函数 g 的形式1t-iw(1-∑k=1∞ake2πibkt)，使得∑k⩾1|ak|e2π|wbk|<1，wbk<0。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applied and Computational Harmonic Analysis 物理-物理：数学物理

CiteScore

5.40

自引率

4.00%

发文量

审稿时长

22.9 weeks

期刊介绍： Applied and Computational Harmonic Analysis (ACHA) is an interdisciplinary journal that publishes high-quality papers in all areas of mathematical sciences related to the applied and computational aspects of harmonic analysis, with special emphasis on innovative theoretical development, methods, and algorithms, for information processing, manipulation, understanding, and so forth. The objectives of the journal are to chronicle the important publications in the rapidly growing field of data representation and analysis, to stimulate research in relevant interdisciplinary areas, and to provide a common link among mathematical, physical, and life scientists, as well as engineers.