Luzin’s Problem on Fourier Convergence and Homeomorphisms

Gady Kozma; Alexander Olevskiĭ

doi:10.1134/S008154382205011X

Luzin’s Problem on Fourier Convergence and Homeomorphisms

Gady Kozma^*, Alexander Olevskiĭ

^*Corresponding author for this work

School of Mathematical Sciences

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

Abstract

Abstract: We show that for every continuous function f there exists an absolutely continuous circle homeomorphism φ such that the Fourier series of f ◦ φ converges uniformly. This resolves a problem posed by N. N. Luzin.

Original language	English
Pages (from-to)	124-168
Number of pages	45
Journal	Proceedings of the Steklov Institute of Mathematics
Volume	319
Issue number	1
DOIs	https://doi.org/10.1134/S008154382205011X
State	Published - Dec 2022

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abstract = "Abstract: We show that for every continuous function f there exists an absolutely continuous circle homeomorphism φ such that the Fourier series of f ◦ φ converges uniformly. This resolves a problem posed by N. N. Luzin.",

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year = "2022",

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Luzin’s Problem on Fourier Convergence and Homeomorphisms

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