Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Generalized summing sequences and the mean ergodic theorem


Authors: Julius Blum and Bennett Eisenberg
Journal: Proc. Amer. Math. Soc. 42 (1974), 423-429
MSC: Primary 28A65; Secondary 22D40
MathSciNet review: 0330412
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Abstract: Conditions are found on a sequence of probability measures $ {\mu _n}$ on a locally compact abelian group G so that, for any strongly continuous unitary representation of G, $ \smallint {U_g}f\;d{\mu _n}$ will converge to a U-invariant function. These conditions are applied in the case where the group is the integers.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1974-0330412-0
Article copyright: © Copyright 1974 American Mathematical Society