On the existence of automorphisms with simple Lebesgue spectrum

Klopotowski, A. ; Nadkarni, M. G. (1999) On the existence of automorphisms with simple Lebesgue spectrum Proceedings of the Indian Academy of Sciences - Mathematical Sciences, 109 (1). pp. 47-55. ISSN 0253-4142

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Official URL: http://www.ias.ac.in/j_archive/mathsci/109/1/47-55...

Related URL: http://dx.doi.org/10.1007/BF02837766

Abstract

It is shown that if T is a measure preserving automorphism on a probability space (Ω,B, m) which admits a random variable X0 with mean zero such that the stochastic sequence X0 o Tn,n ε Z is orthonormal and spans L02(Ω,B,m), then for any integer k ≠ 0, the random variables X o Tnk,n ε Z generate B modulom.

Item Type:Article
Source:Copyright of this article belongs to Indian Academy of Sciences.
Keywords:Dynamical System; Simple Lebesgue Spectrum; Walsh Function
ID Code:23432
Deposited On:25 Nov 2010 09:16
Last Modified:17 May 2016 07:15

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