Generation of analytic semigroups by generalized Ornstein–Uhlenbeck operators with potentials

AbstractIt is shown that the generalized Ornstein–Uhlenbeck operator “with potential” AΦ,G,Vu:=Δu−∇Φ⋅∇u+G⋅∇u−Vu with suitable domain generates an analytic semigroup on the weighted space Lp(RN,μ), 1<p<∞, where μ(dx)=e−Φdx. The result extends the generation theorem established by Metafune–Prüss–Rhandi–Schnaubelt when V≡0 to the case where V≢0, while the proof is based on their useful theorem that a class of second order elliptic operators generates an analytic semigroup on the unweighted space Lp(RN)