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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A class of ergodic transformations having simple spectrum


Author: J. R. Baxter
Journal: Proc. Amer. Math. Soc. 27 (1971), 275-279
MSC: Primary 28.70; Secondary 47.00
MathSciNet review: 0276440
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Abstract: A class of ergodic, measure-preserving, invertible point transformations is defined, called class $ S$. Any measure-preserving point transformation induces a unitary operator on the Hilbert space of $ {\mathcal{L}_2}$-functions. A theorem is proved here which implies that the operator induced by any transformation in class $ S$ has simple spectrum. [It is then a known result that the transformations in class $ S$ have zero entropy.]


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DOI: https://doi.org/10.1090/S0002-9939-1971-0276440-2
Keywords: Ergodic point transformation, simple spectrum, zero entropy, stacking method
Article copyright: © Copyright 1971 American Mathematical Society