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On functions that are trivial cocycles for a set of irrationals


Author: Larry Baggett
Journal: Proc. Amer. Math. Soc. 104 (1988), 1212-1215
MSC: Primary 28D05; Secondary 42A05, 58F11
DOI: https://doi.org/10.1090/S0002-9939-1988-0948145-6
MathSciNet review: 948145
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Abstract: The main result of this paper is that the set of irrationals, for which a given function is a trivial cocycle, must be of the first category, unless the function is the exponential of a trigonometric polynomial.


References [Enhancements On Off] (What's this?)

  • [1] J. Aaronson and M. Nadkarni, $ {L_\infty }$ eigenvalues and $ {L_2}$ spectra of nonsingular transformations (to appear).
  • [2] L. Baggett and K. Merrill, Equivalence of cocycles for an irrational rotation (to appear).
  • [3] Henry Helson and Kathy D. Merrill, Cocycles on the circle. II, Special classes of linear operators and other topics (Bucharest, 1986) Oper. Theory Adv. Appl., vol. 28, Birkhäuser, Basel, 1988, pp. 121–124. MR 942917

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0948145-6
Article copyright: © Copyright 1988 American Mathematical Society