A non-singular transformation whose spectrum has Lebesgue component of multiplicity one
Dynamical Systems
2019-02-20 v2 Complex Variables
Spectral Theory
Abstract
In this note we give an example of an ergodic non-singular map whose unitary operator admits a Lebesgue component of multiplicity one in its spectrum.
Keywords
Cite
@article{arxiv.1402.1312,
title = {A non-singular transformation whose spectrum has Lebesgue component of multiplicity one},
author = {E. H. El Abdalaoui and M. G. Nadkarni},
journal= {arXiv preprint arXiv:1402.1312},
year = {2019}
}
Comments
The paper is accepted for publication in ETDS, and in this revised version, we gives a short proof of a new Lemma of L^1-flatness that state that if the spectral type of generalized odometer (rank one maps in particular case) has the same null sets as the Lebesgue measure then the associated sequence of polynomials is L^1-flat