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

It 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