This article is cited in 28 papers

On Walsh series with monotone coefficients

G. G. Gevorkyan^a, K. A. Navasardyan<sup>b

a</sup> Institute of Mathematics, National Academy of Sciences of Armenia
^b Yerevan State University

Abstract: We prove that if $a_n\downarrow 0$ and $\sum_{n=0}^\infty a_n^2=+\infty$ then the Walsh series $\sum_{n=0}^\infty a_nW_n(x)$ has the following property. For any measurable function $f(x)$ which is finite almost everywhere, there are numbers $\delta_n=0,\pm 1$ such that the series $\sum_{n=0}^\infty\delta_na_nW_n(x)$ converges to $f(x)$ almost everywhere. This assertion complements and strengthens previously known results about universal Walsh series and Walsh null-series.

MSC: 42C10

Received: 30.09.1997

DOI: 10.4213/im227

 English version: Izvestiya: Mathematics, 1999, 63:1, 37–55

Bibliographic databases:

• 
• 
• 
•