Weighted β−absolute Convergence of Single and Double Walsh−Fourier Series of Functions of Φ − ∧ −BV

Q4 Mathematics Journal of the Indian Mathematical Society Pub Date : 2018-12-12 DOI:10.18311/JIMS/2019/22561

K. N. Darji, R. Vyas

引用次数: 1

Abstract

For one variable function of Φ − ∧−bounded variation on [0,1] the sufficient condition for the weighted β−absolute convergence of its Walsh−Fourier series ∑ m γ m | ˆ f(m)| β , where 0 < β < 2 and {γ m } is a weighted sequence, is obtained and is extended for two dimensional analogue.

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Φ−∧−BV函数的单、双Walsh−傅立叶级数的加权β−绝对收敛性

对于在[0,1]上Φ−∧−有界变分的一元函数，得到了其Walsh - Fourier级数∑m γ m |} f(m)| β的加权β−绝对收敛的充分条件，其中0 < β < 2且{γ m}是一个加权序列。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of the Indian Mathematical Society Mathematics-Mathematics (all)

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0.50

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期刊介绍： The Society began publishing Progress Reports right from 1907 and then the Journal from 1908 (The 1908 and 1909 issues of the Journal are entitled "The Journal of the Indian Mathematical Club"). From 1910 onwards,it is published as its current title ''the Journal of Indian Mathematical Society. The four issues of the Journal constitute a single volume and it is published in two parts: issues 1 and 2 (January to June) as one part and issues 3 and 4 (July to December) as the second part. The four issues of the Mathematics Student (another periodical of the Society) are published as a single yearly volume. Only the original research papers of high quality are published in the Journal of Indian Mathematical Society.