Uniqueness Theorems for Multiple Series by Vilenkin and Generalized Haar Systems

Authors

  • Karen Navasardyan Yerevan State University

DOI:

https://doi.org/10.52737/18291163-2018.10.6-1-15

Keywords:

Uniqueness Theorem, Summation Method, Vilenkin System, Haar System, Fourier Series

Abstract

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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Published

2018-07-09 — Updated on 2022-09-19

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How to Cite

Uniqueness Theorems for Multiple Series by Vilenkin and Generalized Haar Systems. (2022). Armenian Journal of Mathematics, 10(6), 1-15. https://doi.org/10.52737/18291163-2018.10.6-1-15 (Original work published 2018)