L1 Convergence of Fourier Transforms Revisited

被引：0

作者：

Liflyand, E. ^{[1
]}

机构：

[1] Bar Ilan Univ, Dept Math, IL-52900 Ramat Gan, Israel

来源：

RESULTS IN MATHEMATICS | 2023年 / 78卷 / 01期

关键词：

Trigonometric series; Fourier transform; bounded variation; integrability; L-1; convergence;

D O I：

10.1007/s00025-022-01782-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The author's recent attempt to generalize the problem of L-1 convergence of trigonometric series to the non-periodic case is finalized here. It can now be said that any known condition which guarantees integrability of the Fourier transform of a function of bounded variation also leads to the L-1 convergence of its partial integrals provided that a universal necessary and sufficient condition is added.

引用

页数：14

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