Uniqueness Theorems for Multiple Series by Vilenkin and Generalized Haar Systems

  • Karen Navasardyan Yerevan State University
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. 

Published
2018-07-09
How to Cite
Navasardyan, K. (2018). Uniqueness Theorems for Multiple Series by Vilenkin and Generalized Haar Systems. Armenian Journal of Mathematics, 10(6), 1-15. Retrieved from http://armjmath.sci.am/index.php/ajm/article/view/169