Note on a result of Kerman and Weit
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.
scientific article; zbMATH DE number 6062113