Spectra of self-similar ergodic actions
Valery V. Ryzhikov
TL;DR
This paper explores the spectral properties of infinite self-similar rank 1 dynamical systems, revealing unusual spectral behaviors in Gaussian and Poisson suspensions through orthogonal operators.
Contribution
It introduces new spectral phenomena in self-similar rank 1 systems and analyzes their implications for Gaussian and Poisson suspensions.
Findings
Unusual spectral properties identified in Gaussian suspensions
Distinct spectral behaviors observed in Poisson suspensions
Orthogonal operators reveal new spectral phenomena
Abstract
This note is devoted to infinite self-similar rank 1 constructions and their applications to the spectral theory of dynamical systems. The properties of orthogonal operators induced by self-similar constructions provide some unusual spectral properties of Gaussian and Poisson suspensions.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Topological and Geometric Data Analysis · advanced mathematical theories