Ukrainian Mathematical Journal

, Volume 49, Issue 3, pp 494–505 | Cite as

Regularity results for Kolmogorov equations in L 2 (H, μ) spaces and applications

  • G. Da Prato


We consider the transition semigroup R t =e tsA associated to an Ornstein—Uhlenbeck process in a Hilbert space H. We characterize, under suitable assumptions, the domain of A as a subspace W2,2 (H, μ), where μ is the invariant measure associated to R t . This characterization is then used to treat some Kolmogorov equations with variable coefficients.


Linear Operator Invariant Measure Regularity Result Dirichlet Form Separable Hilbert Space 
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© Plenum Publishing Corporation 1998

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  • G. Da Prato

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