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

Author(s): Lawrence W. Baggett; Herbert A. Medina; Kathy D. Merrill
Journal: Proc. Amer. Math. Soc. 124 (1996), 89-93.
MSC (1991): Primary 28D05, 11K38
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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:

[B]: L. Baggett, On functions that are trivial for a set of irrationals, Proc. Amer. Math. Soc. 104 (1988), 1212--1215. MR 89h:28022a
[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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