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April 2016 On the existence of universal series by the generalized Walsh system
Sergo A. Episkoposian
Banach J. Math. Anal. 10(2): 415-429 (April 2016). DOI: 10.1215/17358787-3589331

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.

Citation

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Sergo A. Episkoposian. "On the existence of universal series by the generalized Walsh system." Banach J. Math. Anal. 10 (2) 415 - 429, April 2016. https://doi.org/10.1215/17358787-3589331

Information

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

zbMATH: 06575518
MathSciNet: MR3489647
Digital Object Identifier: 10.1215/17358787-3589331

Subjects:
Primary: 42A65
Secondary: 42A20, 42C10

Rights: Copyright © 2016 Tusi Mathematical Research Group

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Vol.10 • No. 2 • April 2016
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