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 Proceedings of the YSU, Physical and Mathematical Sciences, 2014, Issue 1, Pages 22–25 (Mi uzeru46)

Mathematics

On Fourier coefficients with respect to the Walsh double system

A. B. Minasyan

Yerevan State University

Abstract: In the present paper we will consider the behavior of Fourier coefficients with respect to the Walsh double system after modification of functions. We prove that for any function $f(x,y)\in L^p[0,1]^2$ one can find a function $g(x,y)\in L^p[0,1]^2$ coinciding with $f(x,y)$ except a set of small measure such that the non-zero coefficients of $g(x,y)$ are monotonically decreasing over all rays in absolute value.

Keywords: Walsh double system, Fourier coefficients.

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MSC: 42A65, 42A20
Accepted:24.03.2014
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Citation: A. B. Minasyan, “On Fourier coefficients with respect to the Walsh double system”, Proceedings of the YSU, Physical and Mathematical Sciences, 2014, no. 1, 22–25

Citation in format AMSBIB
\Bibitem{Min14}
\by A.~B.~Minasyan
\paper On Fourier coefficients with respect to the Walsh double system
\jour Proceedings of the YSU, Physical and Mathematical Sciences
\yr 2014
\issue 1
\pages 22--25
\mathnet{http://mi.mathnet.ru/uzeru46}