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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On bounded solutions to convolution equations
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by Enrico Priola and Jerzy Zabczyk PDF
Proc. Amer. Math. Soc. 134 (2006), 3275-3286 Request permission

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
  • 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
  • © Copyright 2006 American Mathematical Society
  • 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
  • MathSciNet review: 2231912