HARMONIC ANALYSIS OF FUNCTIONS PERIODIC AT INFINITY

被引：0

作者：

Baskakov, A. ^{[1
]}

Strukova, I. ^{[1
]}

机构：

[1] Voronezh State Univ, Fac Appl Math Mech & Informat, 1 Univ Skaya Sq, Voronezh 394036, Russia

来源：

EURASIAN MATHEMATICAL JOURNAL | 2016年 / 7卷 / 04期

基金：

俄罗斯科学基金会; 俄罗斯基础研究基金会;

关键词：

Banach space; functions slowly varying at infinity; functions periodic at infinity; Wiener's theorem; absolutely convergent Fourier series; invertibility; difference equations;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we introduce the notion of vector-valued functions periodic at infinity. We characterize the sums of the usual periodic functions and functions vanishing at infinity as a subclass of these functions. Our main focus is the development of the basic harmonic analysis for functions periodic at infinity and an analogue of the celebrated Wiener's Lemma that deals with absolutely convergent Fourier series. We also derive criteria of periodicity at infinity for solutions of difference and differential equations. Some of the results are derived by means of the spectral theory of isometric group representations.

引用

页码：9 / 29

页数：21

共 29 条

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