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Shifted generalized Mehler semigroup on white noise functionals

Shifted generalized Mehler semigroup on white noise functionals

We study shifted generalized Mehler semigroups on white noise functionals.We prove characterizations of invariant (white noise) distribution and the covariance property for shifted generalized Mehler semigroups.Also, we prove a Liouville type property of a shifted generalized Mehler semigroup or its infinitesimal generator.