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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2018, Volume 303, Pages 186–192
DOI: https://doi.org/10.1134/S0371968518040143
(Mi tm3946)
 

Uniformly convergent Fourier series and multiplication of functions

V. V. Lebedev

National Research University Higher School of Economics, ul. Tallinskaya 34, Moscow, 123458 Russia
References:
Abstract: Let $U(\mathbb T)$ be the space of all continuous functions on the circle $\mathbb T$ whose Fourier series converges uniformly. Salem's well-known example shows that a product of two functions in $U(\mathbb T)$ does not always belong to $U(\mathbb T)$ even if one of the factors belongs to the Wiener algebra $A(\mathbb T)$. In this paper we consider pointwise multipliers of the space $U(\mathbb T)$, i.e., the functions $m$ such that $mf\in U(\mathbb T)$ whenever $f\in U(\mathbb T)$. We present certain sufficient conditions for a function to be a multiplier and also obtain some Salem-type results.
Keywords: uniformly convergent Fourier series, function spaces, multiplication operators.
Received: April 1, 2018
English version:
Proceedings of the Steklov Institute of Mathematics, 2018, Volume 303, Pages 171–177
DOI: https://doi.org/10.1134/S008154381808014X
Bibliographic databases:
Document Type: Article
UDC: 517.51
MSC: 42A20, 42A45, 42B35
Language: Russian
Citation: V. V. Lebedev, “Uniformly convergent Fourier series and multiplication of functions”, Harmonic analysis, approximation theory, and number theory, Collected papers. Dedicated to Academician Sergei Vladimirovich Konyagin on the occasion of his 60th birthday, Trudy Mat. Inst. Steklova, 303, MAIK Nauka/Interperiodica, Moscow, 2018, 186–192; Proc. Steklov Inst. Math., 303 (2018), 171–177
Citation in format AMSBIB
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\by V.~V.~Lebedev
\paper Uniformly convergent Fourier series and multiplication of functions
\inbook Harmonic analysis, approximation theory, and number theory
\bookinfo Collected papers. Dedicated to Academician Sergei Vladimirovich Konyagin on the occasion of his 60th birthday
\serial Trudy Mat. Inst. Steklova
\yr 2018
\vol 303
\pages 186--192
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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\crossref{https://doi.org/10.1134/S0371968518040143}
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    Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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