Integrability and Convergence of Trigonometric Series and Fourier Transforms

Elijah Liflyand

doi:10.1007/978-3-031-62894-8_12

Integrability and Convergence of Trigonometric Series and Fourier Transforms

Elijah Liflyand

Department of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

A general overview is given for whether a trigonometric series is the Fourier series of an integrable function and when such a series can be approximated in L¹ by its partial sums. This is a necessary preliminary for the attempt to generalize the problem of L¹ convergence of trigonometric series to the non-periodic case, which is the main instance of the present study.

Original language	English
Title of host publication	Trends in Mathematics
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	121-130
Number of pages	10
DOIs	https://doi.org/10.1007/978-3-031-62894-8_12
State	Published - 2024

Publication series

Name	Trends in Mathematics
Volume	7
ISSN (Print)	2297-0215
ISSN (Electronic)	2297-024X

Bibliographical note

Publisher Copyright:
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.

Keywords

Bounded variation
Fourier transform
Integrability
L convergence
Trigonometric series

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10.1007/978-3-031-62894-8_12

Cite this

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Integrability and Convergence of Trigonometric Series and Fourier Transforms

Abstract

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Keywords

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