A class of ergodic transformations having simple spectrum

J. R. Baxter

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24 Scopus citations

Abstract

A class of ergodic, measure-preserving, invertible point transformations is defined, called class S. Any measurepreserving point transformation induces a unitary operator on the Hilbert space of ℒ2-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.].

Original languageEnglish (US)
Pages (from-to)275-279
Number of pages5
JournalProceedings of the American Mathematical Society
Volume27
Issue number2
DOIs
StatePublished - Feb 1971

Keywords

  • Ergodic point transformation
  • Simple spectrum
  • Stacking method
  • Zero entropy

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