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On bounded solutions to convolution equations


Authors: Enrico Priola and Jerzy Zabczyk
Journal: Proc. Amer. Math. Soc. 134 (2006), 3275-3286
MSC (2000): Primary 43A55, 68B15, 47D07, 31C05
DOI: https://doi.org/10.1090/S0002-9939-06-08608-4
Published electronically: May 8, 2006
MathSciNet review: 2231912
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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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Additional Information

Enrico Priola
Affiliation: Dipartimento di Matematica, Università di Torino, via Carlo Alberto 10, 10123, Torino, Italy
Email: priola@dm.unito.it

Jerzy Zabczyk
Affiliation: Instytut Matematyczny, Polskiej Akademii Nauk, ul. Sniadeckich 8, 00-950, War- szawa, Poland
Email: zabczyk@impan.gov.pl

DOI: https://doi.org/10.1090/S0002-9939-06-08608-4
Keywords: Convolution equations on groups, bounded harmonic functions, L\'evy processes
Received by editor(s): May 25, 2005
Published electronically: May 8, 2006
Additional Notes: The first author was partially supported by Italian National Project MURST “Equazioni di Kolmogorov” and by Contract No ICA1-CT-2000-70024 between European Community and the Stefan Banach International Mathematical Center in Warsaw.
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2006 American Mathematical Society

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