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Using extrapolation spaces introduced by Da Prato-Grisvard and Nagel we prove a non-autonomous perturbation theorem for Hille-Yosida operators. The abstract result is applied to non-autonomous retarded partial differential equations.
We show that the domain of the Ornstein-Uhlenbeck operator on
equals the weighted Sobolev space , where is the corresponding invariant measure. Our approach relies on the operator sum method, namely the commutative and the non commutative Dore-Venni theorems.
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