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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2022, Volume 319, Pages 134–181
DOI: https://doi.org/10.4213/tm4263 (Mi tm4263) 		 
Luzin's Problem on Fourier Convergence and Homeomorphisms

Gady Kozmaa, Alexander Olevskiĭb

a Department of Mathematics, The Weizmann Institute of Science, 234 Herzl Street, Rehovot, 7610001, Israel
b School of Mathematical Sciences, Tel Aviv University, Tel Aviv, 69978, Israel
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DOI: https://doi.org/10.4213/tm4263
Abstract: We show that for every continuous function $f$ there exists an absolutely continuous circle homeomorphism $\phi $ such that the Fourier series of $f\circ \phi $ converges uniformly. This resolves a problem posed by N. N. Luzin.
Funding agency Grant number
Israel Science Foundation
Jesselson Foundation
The work of the first author was supported by the Israel Science Foundation and by the Jesselson Foundation.
Received: November 14, 2021
Revised: February 8, 2022
Accepted: March 18, 2022
Published: 31.01.2023
English version:
Proceedings of the Steklov Institute of Mathematics, 2022, Volume 319, Pages 124–168
DOI: https://doi.org/10.1134/S008154382205011X
Bibliographic databases:
Document Type: Article
UDC: 517.51
Language: Russian
Citation: Gady Kozma, Alexander Olevskiǐ, “Luzin's Problem on Fourier Convergence and Homeomorphisms”, Approximation Theory, Functional Analysis, and Applications, Collected papers. On the occasion of the 70th birthday of Academician Boris Sergeevich Kashin, Trudy Mat. Inst. Steklova, 319, Steklov Math. Inst., Moscow, 2022, 134–181; Proc. Steklov Inst. Math., 319 (2022), 124–168
Citation in format AMSBIB
\Bibitem{KozOle22}
\by Gady~Kozma, Alexander~Olevski{\v\i}
\paper Luzin's Problem on Fourier Convergence and Homeomorphisms
\inbook Approximation Theory, Functional Analysis, and Applications
\bookinfo Collected papers. On the occasion of the 70th birthday of Academician Boris Sergeevich Kashin
\serial Trudy Mat. Inst. Steklova
\yr 2022
\vol 319
\pages 134--181
\publ Steklov Math. Inst.
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4263}
\crossref{https://doi.org/10.4213/tm4263}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2022
\vol 319
\pages 124--168
\crossref{https://doi.org/10.1134/S008154382205011X}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85148447702}
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
     
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