R. A. Konev, V. V. Ryzhikov, “On the Collection of Spectral Multiplicities $\{2,4,\dots,2^n\}$ for Totally Ergodic $\mathbb{Z}^2$-Actions”, Mat. Zametki, 2014, Volume 96, Issue 3,Pages 383

This article is cited in 3 papers

On the Collection of Spectral Multiplicities $\{2,4,\dots,2^n\}$ for Totally Ergodic $\mathbb{Z}^2$-Actions

R. A. Konev, V. V. Ryzhikov

M. V. Lomonosov Moscow State University

Abstract: The paper is devoted to the realization of collections of spectral multiplicities for ergodic $\mathbb{Z}^2$-actions. Sufficient conditions ensuring the realizability of multiplicities of the form $\{2,4,\dots,2^n\}$ are given.

Keywords: collection of spectral multiplicities $\{2,4,\dots,2^n\}$, ergodic $\mathbb{Z}^2$-action, spectral multiplicity of an ergodic action, linear envelope, cyclic vector.

UDC: 517.987

Received: 24.12.2012
Revised: 09.04.2014

DOI: 10.4213/mzm10191