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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
MathSciNet review:
1285971
Full-text PDF Free Access
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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- cobounding function is constructed.
- [B]
Larry
Baggett, On functions that are trivial cocycles
for a set of irrationals, Proc. Amer. Math.
Soc. 104 (1988), no. 4, 1212–1215. MR 948145
(89h:28022a), http://dx.doi.org/10.1090/S0002-9939-1988-0948145-6
- [BM1]
Larry
Baggett and Kathy
Merrill, Representations of the Mautner group and cocycles of an
irrational rotation, Michigan Math. J. 33 (1986),
no. 2, 221–229. MR 837580
(87h:22011), http://dx.doi.org/10.1307/mmj/1029003351
- [BM2]
L.
Baggett and K.
Merrill, Smooth cocycles for an irrational rotation, Israel J.
Math. 79 (1992), no. 2-3, 281–288. MR 1248918
(95e:28017), http://dx.doi.org/10.1007/BF02808220
- [H]
Michael-Robert
Herman, Sur la conjugaison différentiable des
difféomorphismes du cercle à des rotations, Inst. Hautes
Études Sci. Publ. Math. 49 (1979), 5–233
(French). MR
538680 (81h:58039)
- [ILR]
A.
Iwanik, M.
Lemańczyk, and D.
Rudolph, Absolutely continuous cocycles over irrational
rotations, Israel J. Math. 83 (1993), no. 1-2,
73–95. MR
1239717 (94i:58108), http://dx.doi.org/10.1007/BF02764637
- [M]
Herbert
A. Medina, Spectral types of unitary operators arising from
irrational rotations on the circle group, Michigan Math. J.
41 (1994), no. 1, 39–49. MR 1260607
(95a:28014), http://dx.doi.org/10.1307/mmj/1029004913
- [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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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:
http://dx.doi.org/10.1090/S0002-9939-96-02990-5
PII:
S 0002-9939(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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