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Explicit Infinite Mixing Automorphisms with Simple Spectra of Symmetric Squares

Sofia V. Vereshchagina, Valery V. Ryzhikov

Abstract

We present mixing ergodic automorphisms of a space with sigma-finite measure whose symmetric tensor squares have simple spectra. This property is of interest in connection with dynamical spectral problems of A.N. Kolmogorov and V.A. Rokhlin. Explicit examples are given in the class of near-Sidon constructions.

Explicit Infinite Mixing Automorphisms with Simple Spectra of Symmetric Squares

Abstract

We present mixing ergodic automorphisms of a space with sigma-finite measure whose symmetric tensor squares have simple spectra. This property is of interest in connection with dynamical spectral problems of A.N. Kolmogorov and V.A. Rokhlin. Explicit examples are given in the class of near-Sidon constructions.
Paper Structure (3 sections, 20 equations)

This paper contains 3 sections, 20 equations.

Table of Contents

  1. Introduction
  2. Automorphisms of the class ${\cal T}_2$
  3. Proof