On the existence of automorphisms with simple Lebesgue spectrum |
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| Authors: | A Kłopotowski M G Nadkarni |
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| Institution: | (1) Institut Galilée, Université Paris XIII, 93430 Villetaneuse cedex, France;(2) Department of Mathematics, University of Mumbai, 400098 Kalina, Mumbai, India |
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| Abstract: | It is shown that ifT 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 L0
2(Ω,B,m), then for any integerk ≠ 0, the random variablesX o Tnk,n ε ℤ generateB modulom. |
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| Keywords: | Dynamical system simple Lebesgue spectrum Walsh function |
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