On the generalized Ornstein-Uhlenbeck operators perturbed by regular potentials and inverse square potentials in weighted L²-spaces
DOI:
https://doi.org/10.22199/issn.0717-6279-5290Keywords:
inverse square potential, regular potential, weighted Hardy inequality, generalized Ornstein-Uhlenbeck operator, C₀-semigroup, bilinear formsAbstract
Generation of a quasi-contractive semigroup by generalized Ornstein-Uhlenbeck operators
ℒ = −∆ + ∇Φ · ∇ − G · ∇ + V + c|x|−2
in the weighted space L2(RN, e−Φ(x)dx) is proven, where Φ ∈ C2(RN, R), G ∈ C1(RN, RN), 0 ≤ V ∈ C1(RN) and c > 0. The proofs are carried out by an application of L2-weighted Hardy inequality and bilinear form techniques.
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