Coefficients of multiple Fourier-Haar series and variational modulus of continuity
Еселi Фурье-Хаар қатарының коэффициенттерi және вариациялық үзiлiссiздiк модулi
Коэффициенты кратного ряда Фурье–Хаара и вариационный модуль непрерывности
Akhazhanov T.B. Bokayev N.А. Matin D.T. Aktosun T.
2023E.A. Buketov Karaganda University Publish house
Bulletin of the Karaganda University. Mathematics Series
2023#112Issue 421 - 29 pp.
In this paper, we introduce the concept of a variational modulus of continuity for functions of several variables, give an estimate for the sum of the coefficients of a multiple Fourier-Haar series in terms of the variational modulus of continuity, and prove theorems of absolute convergence of series composed of the coefficients of multiple Fourier-Haar series. In this paper, we study the issue of the absolute convergence for multiple series composed of the Fourier-Haar coefficients of functions of several variables of bounded p-variation. We estimate the coefficients of a multiple Fourier-Haar series in terms of the variational modulus of continuity and prove the sufficiency theorem for the condition for the absolute convergence of series composed of the Fourier-Haar coefficients of the considered function class. This paper researches the question: under what conditions, imposed on the variational modulus of continuity of the fractional order of several variables functions, there is the absolute convergence for series composed of the coefficients of multiple Fourier-Haar series.
coefficients of multiple Fourier-Haar series , Fourier-Haar series , variational modulus of continuity
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L.N. Gumilyov Eurasian National University, Astana, Kazakhstan
The University of Texas at Arlington, Arlington, United States
L.N. Gumilyov Eurasian National University
The University of Texas at Arlington
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