L1 Convergence of Fourier Transforms Revisited

E. Liflyand

doi:10.1007/s00025-022-01782-6

L¹ Convergence of Fourier Transforms Revisited

E. Liflyand

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

The author’s recent attempt to generalize the problem of L¹ 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 L¹ convergence of its partial integrals provided that a universal necessary and sufficient condition is added.

Original language	English
Article number	1
Journal	Results in Mathematics
Volume	78
Issue number	1
DOIs	https://doi.org/10.1007/s00025-022-01782-6
State	Published - Feb 2023

Bibliographical note

Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

Keywords

Fourier transform
L convergence
Trigonometric series
bounded variation
integrability

Access to Document

10.1007/s00025-022-01782-6

Cite this

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