Fourier Coefficients of Functions with a Given Modulus of Continuity

V. S. Biryukova

M. V. Lomonosov Moscow State University

Abstract: In this paper, we study the role of the convexity condition for the modulus of continuity in the problem of finding an upper bound for the Fourier coefficients taken over the class of functions with a given modulus of continuity. Also, we solve the problem of the Fourier coefficients for the Rademacher system.

Keywords: Fourier coefficient, modulus of continuity of a function, system of Rademacher functions, $2\pi$-periodic function, convex function.

UDC: 517.518.454

Received: 11.05.2006

DOI: 10.4213/mzm3546

 English version: Mathematical Notes, 2007, 81:2, 164–171

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