Uniqueness theorems for simple trigonometric series with application to multiple series

IF 0.8 4区数学 Q2 MATHEMATICS

Sbornik Mathematics Pub Date : 2021-01-01 DOI:10.1070/SM9525

G. G. Gevorkyan

引用次数: 1

Abstract

For simple trigonometric series it is shown, in particular, that if the trigonometric series is Riemann summable in measure to an integrable function and if the Riemann majorant is finite everywhere except possibly on a countable set, then this series is the Fourier series of the function . Uniqueness theorems for multiple trigonometric series are obtained on the basis of this result. Bibliography: 14 titles.

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简单三角级数的唯一性定理及其在多重级数中的应用

对于简单的三角级数，特别地，如果这个三角级数在一个可积函数的尺度上是黎曼可和的，如果黎曼主要级数除了可能在可数集合上是有限的，那么这个级数就是这个函数的傅立叶级数。在此基础上，得到了多个三角级数的唯一性定理。参考书目:14篇。

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

Sbornik Mathematics 数学-数学

CiteScore

1.40

自引率

12.50%

发文量

审稿时长

6-12 weeks

期刊介绍： The Russian original is rigorously refereed in Russia and the translations are carefully scrutinised and edited by the London Mathematical Society. The journal has always maintained the highest scientific level in a wide area of mathematics with special attention to current developments in: Mathematical analysis Ordinary differential equations Partial differential equations Mathematical physics Geometry Algebra Functional analysis