A non-singular transformation whose spectrum has Lebesgue component of multiplicity one

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.

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

Cited by in corpus (4)

• Some Notes on Flat Polynomials
• On the Erdös flat polynomials problem, Chowla conjecture and Riemann Hypothesis
• On the spectral type of rank one flows and Banach problem with calculus of generalized Riesz products on the real line
• On the Mahler measure of the spectrum of rank one maps