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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Stability of group representations and Haar spectrum


Authors: Robert Azencott and William Parry
Journal: Trans. Amer. Math. Soc. 172 (1972), 317-327
MSC: Primary 22D10; Secondary 28A65
MathSciNet review: 0310128
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Abstract: If $ U$ and $ V$ are commuting unitary representations of locally compact abelian groups $ S$ and $ T$, new representations of $ S$ (perturbations of $ U$) can be obtained from composition with images of $ U$ in $ V$. If most of these representations are equivalent to $ U,U$ is said to be $ V$ stable. We investigate conditions which, together with stability, ensure that $ U$ has (uniform) Haar spectrum. The principal applications are to dynamical systems which possess auxiliary groups with respect to which motion is stable.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1972-0310128-X
PII: S 0002-9947(1972)0310128-X
Keywords: Representations stable with respect to another, representations very stable with respect to another, spectral multiplicity, uniform multiplicity, Haar spectrum, maximal spectral type, horocycle flow, nilflow, Weyl commutation relation
Article copyright: © Copyright 1972 American Mathematical Society