On null-series by double Walsh system
type: Item
instance of: scholarly article
title: On null-series by double Walsh system
zbMATH Open document ID: 0832.42018
author: K. A. Navasardyan
published in: Journal of Contemporary Mathematical Analysis. Armenian Academy of Sciences
publication date: 1995-10-18T00:00:00Z
review text: The author obtains 2-dimensional analogues of certain 1-dimensional results of \textit{G. G. Gevorkian} [Anal. Math. 14, No. 3, 219-251 (1988; Zbl 0713.42025)]. For example, he proves that if \(\varepsilon_{mn}\) satisfies certain growth conditions (which include a mild monotone property) and \(\sum \varepsilon^2_{mn} = \infty\), then there is a subset \(E\) of the unit square of two-dimensional Lebesgue measure zero such that given any double Walsh series, which converges to zero except possibly on countably many line segments parallel to the axes, whose coefficients satisfy \(b_{mn} = o(\varepsilon_{mn})\), it must be the case that \(b_{mn} = 0\) for all \(m\) and \(n\). He also shows this result is false if \(b_{mn} = o (\varepsilon_{ mn})\) is replaced by \(b_{mn} = O (\varepsilon_{mn})\). The proof is constructive and somewhat complicated. It relies on the uniqueness result of \textit{H. O. Movsisjan} [Izv. Akad. Nauk. Arm. SSR, Mat. 9, 40-61 (1974; Zbl 0294.42009)].
Mathematics Subject Classification ID: 42C10
zbMATH DE Number: 795431
zbMATH Keywords: uniqueness
zbMATH Keywords: G. G. Gevorkyan
zbMATH Keywords: Walsh series
reviewed by: William R. Wade
MaRDI profile type: Publication
Recommended article: Q4880856
Recommended article: Universality properties of a double series by the generalized Walsh system
Recommended article: Double Walsh series with coefficients of bounded variation
Recommended article: Q4008818
Recommended article: Q3689645
Recommended article: On coefficients of null-series and on sets of uniqueness of trigonometric and Walsh systems
Recommended article: Universal series by multiple Walsh system
Recommended article: On the existence of universal series by the generalized Walsh system
Recommended article: On the integrability of double Walsh series with special coefficients
Recommended article: Double Walsh series with coefficients of bounded variation of higher order
description: scientific article; zbMATH DE number 795431