On bounded solutions to convolution equations

Periodicity of bounded solutions for convolution equations on a separable abelian metric group G is established, and related Liouville type theorems are obtained. A non-constant Borel and bounded harmonic function is constructed for an arbitrary convolution semigroup on any infinite-dimensional sepa...

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2006-11, Vol.134 (11), p.3275-3286
Main Authors: PRIOLA, Enrico, ZABCZYK, Jerzy
Format: Article
Language:English
Subjects:
Abstract harmonic analysis
Applied mathematics
Density
Dirac measures
Exact sciences and technology
Harmonic functions
Hilbert spaces
Mathematical analysis
Mathematical functions
Mathematical theorems
Mathematics
Operator theory
Potential theory
Sciences and techniques of general use
Semigroups
Separable spaces
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Summary:Periodicity of bounded solutions for convolution equations on a separable abelian metric group G is established, and related Liouville type theorems are obtained. A non-constant Borel and bounded harmonic function is constructed for an arbitrary convolution semigroup on any infinite-dimensional separable Hilbert space, generalizing a classical result by Goodman (1973).
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-06-08608-4