Banach Journal of Mathematical Analysis

On the existence of universal series by the generalized Walsh system

Sergo A. Episkoposian

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Abstract

In this paper, we prove the following: let ω(t) be a continuous function with ω(+0)=0 and increasing in [0,). Then there exists a series of the form

k=1ckψk(x)withk=1ck2ω(|ck|)<with the following property: for each ε>0 a weight function μ(x), 0<μ(x)1, |{x[0,1):μ(x)1}|<ε can be constructed so that the series is universal in the weighted space Lμ1[0,1) both with respect to rearrangements and subseries.

Article information

Source
Banach J. Math. Anal., Volume 10, Number 2 (2016), 415-429.

Dates
Received: 12 March 2015
Accepted: 22 July 2015
First available in Project Euclid: 19 April 2016

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1461091167

Digital Object Identifier
doi:10.1215/17358787-3589331

Mathematical Reviews number (MathSciNet)
MR3489647

Zentralblatt MATH identifier
06575518

Subjects
Primary: 42A65: Completeness of sets of functions
Secondary: 42A20: Convergence and absolute convergence of Fourier and trigonometric series 42C10: Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)

Keywords
generalized Walsh system weighted space universal series

Citation

Episkoposian, Sergo A. On the existence of universal series by the generalized Walsh system. Banach J. Math. Anal. 10 (2016), no. 2, 415--429. doi:10.1215/17358787-3589331. https://projecteuclid.org/euclid.bjma/1461091167


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