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The domain of the Ornstein-Uhlenbeck operator on an \(L^p\)-space with invariant measure. (English) Zbl 1170.35375
Summary: We show that the domain of the Ornstein-Uhlenbeck operator on \(L^p\) \((\mathbb{R}^,\mu dx)\) equals the weighted Sobolev space \(W^{2,p} (\mathbb{R}^N,\mu dx)\), where \(\mu dx\) is the corresponding invariant measure. Our approach relies on the operator sum method, namely the commutative and the non commutative Dore-Venni theorems.

MSC:
35J15 Second-order elliptic equations
35K10 Second-order parabolic equations
47A55 Perturbation theory of linear operators
47D06 One-parameter semigroups and linear evolution equations
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