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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A class of ergodic transformations having simple spectrum
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by J. R. Baxter PDF
Proc. Amer. Math. Soc. 27 (1971), 275-279 Request permission

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.]
References
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Additional Information
  • © Copyright 1971 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 27 (1971), 275-279
  • MSC: Primary 28.70; Secondary 47.00
  • DOI: https://doi.org/10.1090/S0002-9939-1971-0276440-2
  • MathSciNet review: 0276440