On bounded solutions to convolution equations

Priola, Enrico; Zabczyk, Jerzy

doi:10.1090/S0002-9939-06-08608-4

On bounded solutions to convolution equations
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by Enrico Priola and Jerzy Zabczyk

Proc. Amer. Math. Soc. 134 (2006), 3275-3286

DOI: https://doi.org/10.1090/S0002-9939-06-08608-4

Published electronically: May 8, 2006

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Abstract:

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).

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On bounded solutions to convolution equations
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Abstract: