On bounded solutions to convolution equations
Enrico Priola, Jerzy Zabczyk · Proceedings of the American Mathematical Society · 2006
Periodicity of bounded solutions for convolution equations on a separable abelian metric group G 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).