An harmonic analysis for operators: F. and M. Riesz theorems
type: Item
instance of: scholarly article
title: An harmonic analysis for operators: F. and M. Riesz theorems
zbMATH Open document ID: 0537.43009
author: U. B. Tewari
author: Shobha Madan
published in: Illinois Journal of Mathematics
publication date: 1984-01-01T00:00:00Z
review text: The authors consider bounded linear operators on a homogeneous Banach space B on a compact Abelian group G, with ordered dual. Following K. DeLeeuw one associates a formal Fourier series with such operators. When \(B=L^ p(G)\), \(1\leq p<\infty\), or \(B=C(G)\) the authors generalize the F. and M. Riesz theorem stating that a power series on the unit circle cannot vanish on a subset having positive Lebesgue measure without vanishing almost everywhere. For certain homogeneous Banach spaces in this setting the authors generalize also the first F. and M. Riesz theorem stating that a measure whose Fourier transform vanishes for negative indices is absolutely continuous.
Mathematics Subject Classification ID: 43A15
Mathematics Subject Classification ID: 43A32
Mathematics Subject Classification ID: 47A99
zbMATH DE Number: 3853715
zbMATH Keywords: F. and M. Riesz theorems
zbMATH Keywords: homogeneous Banach space
reviewed by: Yoram Sagher
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3853715