Variational modulus of continuity and coefficients of the double Fourier-Haar series

2015

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DOI 10.1063/1.4930455
Data confidence 70 medium
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Abstract

In this paper, the notion of variational modulus of continuity of a function in two variables is introduced. An estimate of the sum of the coefficients of the double Fourier-Haar series via the variational modulus of continuity is given. Theorems on absolute convergence of series containing the coefficients of double Fourier-Haar series are proved.