On entire functions restricted to intervals, partition of unities, and dual Gabor frames

被引：9

作者：

Christensen, Ole ^{[1
]}

Kim, Hong Oh ^{[2
]}

Kim, Rae Young ^{[3
]}

机构：

[1] Tech Univ Denmark, Dept Appl Math & Comp Sci, DK-2800 Lyngby, Denmark

[2] UNIST, Div Gen Studies, Ulsan 689798, South Korea

[3] Yeungnam Univ, Dept Math, Gyongsan 712749, Gyeongbuk, South Korea

来源：

APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS | 2015年 / 38卷 / 01期

基金：

新加坡国家研究基金会;

关键词：

Entire functions; Trigonometric polynomials; Partition of unity; Dual frame pairs; Gabor systems; Tight frames; WEYL-HEISENBERG-FRAMES; BARGMANN-FOCK SPACE; DENSITY THEOREMS; REPRESENTATIONS; INTERPOLATION;

D O I：

10.1016/j.acha.2014.03.005

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Partition of unities appears in many places in analysis. Typically it is generated by compactly supported functions with a certain regularity. In this paper we consider partition of unities obtained as integer-translates of entire functions restricted to finite intervals. We characterize the entire functions that lead to a partition of unity in this way, and we provide characterizations of the "cut-off" entire functions, considered as functions of a real variable, to have desired regularity. In particular we obtain partition of unities generated by functions with small support and desired regularity. Applied to Gabor analysis this leads to constructions of dual pairs of Gabor frames with low redundancy, generated by trigonometric polynomials with small support and desired regularity. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：72 / 86

页数：15

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