Polynomial rigidity and the spectra of Sidon automorphisms

Abstract

Continuum many spectrally disjoint Sidon automorphisms with tensor square isomorphic to a planar translation are produced. Their spectra do not have the group property. To show that their spectra are singular the polynomial rigidity of operators is used, which is related to the concept of linear determinism in the sense of Kolmogorov. In the class of mixing Gaussian and Poisson suspensions over Sidon automorphisms new sets of spectral multiplicities are realized. Bibliography: 12 titles.