We study a new class of Markov-type semigroups (not strongly continuous in general) in the space of all real, uniformly continuous and bounded functions on a separable metric space $E$. Our results allow us to characterize the generators of Markov transition semigroups in infinite dimensions such as the heat and the Ornstein-Uhlenbeck semigroups.
On a class of Markov type semigroups in spaces of uniformly continuous and bounded functions
PRIOLA, Enrico
1999-01-01
Abstract
We study a new class of Markov-type semigroups (not strongly continuous in general) in the space of all real, uniformly continuous and bounded functions on a separable metric space $E$. Our results allow us to characterize the generators of Markov transition semigroups in infinite dimensions such as the heat and the Ornstein-Uhlenbeck semigroups.
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