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On bounded solutions to convolution equations |
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| Authors: | Enrico Priola Jerzy Zabczyk |
| Institution: | Dipartimento di Matematica, Università di Torino, via Carlo Alberto 10, 10123, Torino, Italy ; Instytut Matematyczny, Polskiej Akademii Nauk, ul. Sniadeckich 8, 00-950, Warszawa, Poland |
| Abstract: | Periodicity of bounded solutions for convolution equations on a separable abelian metric group  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). |
| Keywords: | Convolution equations on groups bounded harmonic functions L\'evy processes |
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