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