Note on a result of Kerman and Weit
type: Item
instance of: scholarly article
title: Note on a result of Kerman and Weit
zbMATH Open document ID: 1247.43010
author: Swagato K. Ray
author: Rudra P. Sarkar
published in: The Journal of Fourier Analysis and Applications
publication date: 2012-07-31T00:00:00Z
full work available at URL: https://arxiv.org/abs/1109.0477
review text: A recent paper by \textit{R. A. Kerman} and \textit{Y. Weit} [J. Fourier Anal. Appl. 16, No. 5, 786--790 (2010; Zbl 1207.42004)] states that if a continuous real valued function on the unit circle has unique maximum or unique minimum, then the span of translates of its nonnegative integral powers is dense in the space of all continuous functions on the unit circle. Based on the same argument, the authors prove an analogue of this result for the groups of Wiener class (which includes all locally compact abelian groups, compact topological groups, groups of polynomial growth, \(ax+b\) group etc., as well as the group \(\mathrm{SL}(2,\mathbb{R})\) which is not in the Wiener class and is of exponential growth). The authors also take up Riemannian symmetric spaces of compact and noncompact types.
reviewed by: Valeriĭ V. Volchkov
Mathematics Subject Classification ID: 43A85
Mathematics Subject Classification ID: 22E30
zbMATH DE Number: 6062113
zbMATH Keywords: Wiener class
zbMATH Keywords: groups of polynomial growth
zbMATH Keywords: \(\mathrm{SL}(2
zbMATH Keywords: \mathbb{R})\)
zbMATH Keywords: symmetric spaces
MaRDI profile type: Publication
OpenAlex ID: W2952421204
arXiv ID: 1109.0477
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DOI: 10.1007/S00041-011-9215-0
description: scientific article; zbMATH DE number 6062113