On the maximal spectral type of nilsystems
type: Item
instance of: scholarly article
title: On the maximal spectral type of nilsystems
author: Ethan M. Ackelsberg
author: Florian Karl Richter
author: Or Shalom
published in: Proceedings of the American Mathematical Society. Series B
publication date: 2024-10-18T00:00:00Z
review text: Generalizing the work of \textit{B. Host} et al. [J. Anal. Math. 124, 261--295 (2014; Zbl 1351.37026)] for \(2\)-step nilsystems and work of \textit{A. M. Stepin} [Usp. Mat. Nauk 24, No. 5(149), 241--242 (1969; Zbl 0216.34501)] under a hypothesis on the homogeneous space, arguments due originally to \textit{W. Parry} [Topology 9, 217--224 (1970; Zbl 0176.20502)] are adapted here to prove that the space of square-integrable functions on an ergodic \(k\)-step nilsystem with \(k\geqslant2\) decomposes into a sum of a discrete spectrum subspace and a subspace with Lebesgue spectrum of infinite multiplicity. As a by-product an alternative proof of the \(k=2\) case is also given.
reviewed by: Thomas B. Ward
Mathematics Subject Classification ID: 37A30
Mathematics Subject Classification ID: 37A17
zbMATH DE Number: 7928682
zbMATH Keywords: Lebesgue spectrum
zbMATH Keywords: nilsystems
MaRDI profile type: Publication
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DOI: 10.1090/BPROC/229
description: scientific article; zbMATH DE number 7928682