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

摘要

Let A = Sigma(i,j)(N) = q(ij)D(ij) + Sigma(i,j=1)(N) b(i,j)x(j)D(i) be a possibly degenerate Ornstein-Uhlen-beck operator in R-N and assume that the associated Markov semigroup has an invariant measure mu. We compute the spectrum of A in L-mu(p) for 1 less than or equal to p < infinity. (C) 2002 Elsevier Science (USA). [References: 26]