On Fourier Series on the Torus and Fourier Transforms

被引：0

作者：

Trigub, R. M. ^{[1
]}

机构：

[1] Donetsk Natl Univ, UA-83114 Donetsk, Ukraine

来源：

MATHEMATICAL NOTES | 2021年 / 110卷 / 5-6期

关键词：

Fourier series of a measure on the torus T-d and functions from L-1 (T-d); variation of a measure; Wiener Banach algebras; positive definite functions; exponential entire functions; (C; 1)-means of Fourier series; Vitali variation; Banach-Alaoglu theorem;

D O I：

10.1134/S0001434621110134

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The question of the representability of a continuous function on R-d in the form of the Fourier integral of a finite Borel complex-valued measure on R-d is reduced in this article to the same question for a simple function. This simple function is determined by the values of the given function on the integer lattice R-d d. For d = 1, this result is already known: it is an inscribed polygonal line. The article also describes applications of the obtained theorems to multiple trigonometric Fourier series.

引用

页码：767 / 772

页数：6

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