Potential Analysis

, Volume 9, Issue 1, pp 91–104 | Cite as

Conservativeness of Semigroups Generated by Pseudo Differntial Operators

  • René L. Schilling
Article

Abstract

Assume that the pseudo differential operator -q(x,D) generates a Fellerian or sub-Markovian semigroup. Under some natural additional conditions on the symbol -q(x,ξ) we prove that the operator -q(x,D) is conservative if and only if q(x,0)≡0.

conservativeness Feller semigroup Markov semigroup pseudo differnetial operator 

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Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • René L. Schilling
    • 1
  1. 1.Mathematisches InstitutUniversität Erlangen, Bismarckstraβe 1 1/2ErlangenGermany

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