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On functions that are trivial cocycles
for a set of irrationals. II


Authors: Lawrence W. Baggett, Herbert A. Medina and Kathy D. Merrill
Journal: Proc. Amer. Math. Soc. 124 (1996), 89-93
MSC (1991): Primary 28D05, 11K38
DOI: https://doi.org/10.1090/S0002-9939-96-02990-5
MathSciNet review: 1285971
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Abstract | References | Similar Articles | Additional Information

Abstract: Two results are obtained about the topological size of the set of irrationals for which a given function is a trivial cocycle. An example of a continuous function which is a coboundary with non-$L^1$ cobounding function is constructed.


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

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  • [BM1] L. Baggett and K. Merrill, Representations of the Mautner group and cocycles of an irrational rotation, Michigan Math. J. 33 (1986), 221--229. MR 87h:22011
  • [BM2] ------, Smooth cocycles for an irrational rotation, Israel J. Math. 79 (1992), 281--288. MR 95e:28017
  • [H] M. Herman, Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations, Inst. Hautes Études Sci. Publ. Math. 49 (1979), 5--234. MR 81h:58039
  • [ILR] A. Iwanik, M. Lemanczyk, and D. Rudolph, Absolutely continuous cocycles over irrational rotations, Israel J. Math. 83 (1993), 73--95. MR 94i:58108
  • [M] H. Medina, Spectral types of unitary operators arising from irrational rotations on the circle group, Michigan Math. J. 41 (1994), 39--49. MR 95a:28014

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Additional Information

Lawrence W. Baggett
Email: baggett@euclid.colorado.edu

Herbert A. Medina
Email: hmedina@lmumail.lmu.edu

Kathy D. Merrill
Email: kmerrill@cc.colorado.edu

DOI: https://doi.org/10.1090/S0002-9939-96-02990-5
Received by editor(s): November 15, 1993
Received by editor(s) in revised form: June 21, 1994
Communicated by: J. Marshall Ash
Article copyright: © Copyright 1996 American Mathematical Society

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