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Some results about dissipativity of Kolmogorov operators. (English) Zbl 0996.47028

Summary: Given a Hilbert space \(H\) with a Borel probability measure \(\nu \), we prove the \(m\)-dissipativity in \(L^1(H, \nu)\) of a Kolmogorov operator \(K\) that is a perturbation, not necessarily of gradient type, of an Ornstein-Uhlenbeck operator.

MSC:

47B25 Linear symmetric and selfadjoint operators (unbounded)
81S20 Stochastic quantization
37L40 Invariant measures for infinite-dimensional dissipative dynamical systems
35K57 Reaction-diffusion equations
70H15 Canonical and symplectic transformations for problems in Hamiltonian and Lagrangian mechanics
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References:

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