Translator Disclaimer
May 2016 A characterization of the Riesz family of shifts of functions on locally compact Abelian groups
N. Mohammadian, R. A. Kamyabi Gol, R. Raisi Tousi
Ann. Funct. Anal. 7(2): 314-325 (May 2016). DOI: 10.1215/20088752-3506016

Abstract

For a locally compact Abelian group G, we give a necessary and sufficient condition for shifts of a function ϕL2(G) to be a Riesz family. Also, for a finite family Φ of compactly supported functions in L2(G), we show that the shifts of Φ constitute a Riesz family if and only if the nets (ϕ(ξη))ηL, ϕΦ, are linearly independent for all ξGˆ.

Citation

Download Citation

N. Mohammadian. R. A. Kamyabi Gol. R. Raisi Tousi. "A characterization of the Riesz family of shifts of functions on locally compact Abelian groups." Ann. Funct. Anal. 7 (2) 314 - 325, May 2016. https://doi.org/10.1215/20088752-3506016

Information

Received: 16 April 2015; Accepted: 15 August 2015; Published: May 2016
First available in Project Euclid: 8 April 2016

zbMATH: 1337.43001
MathSciNet: MR3484385
Digital Object Identifier: 10.1215/20088752-3506016

Subjects:
Primary: 43A15
Secondary: 43A25

Rights: Copyright © 2016 Tusi Mathematical Research Group

JOURNAL ARTICLE
12 PAGES


SHARE
Vol.7 • No. 2 • May 2016
Back to Top