Spectrum of Ornstein-Uhlenbeck operators in Lp spaces with respect to invariant measures

Abstract

Let A = ∑i,j=1N qijDij + ∑i,j=1N bij xjDi be a possibly degenerate Ornstein-Uhlenbeck operator in RN and assume that the associated Markov semigroup has an invariant measure μ. We compute the spectrum of A in LμP for 1 ≤ p < ∞. © 2002 Elsevier Science (USA).