Vilenkin和广义Haar系统的多重级数的唯一性定理

IF 0.5 Q3 MATHEMATICS Armenian Journal of Mathematics Pub Date : 2018-07-09 DOI:10.52737/18291163-2018.10.6-1-15

K. Navasardyan

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摘要

本文讨论了关于Vilenkin和广义Haar系统的多级数求和方法的唯一性。证明了如果关于这些系统的多重级数可由该方法求和到$[0,1）^d$上的可积函数，并满足一个额外条件，则它是该函数的傅立叶级数。

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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Uniqueness Theorems for Multiple Series by Vilenkin and Generalized Haar Systems

In this paper we discuss the uniqueness property of a summation method for multiple series with respect to Vilenkin and generalized Haar systems. It is proved that if the multiple series with respect to these systems is a.e. summable by that method to an integrable function on $[0,1)^d$ and satisfies an extra condition, then it is the Fourier series of this function.

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