, Volume 9, Issue 1, pp 91-104

Conservativeness of Semigroups Generated by Pseudo Differntial Operators

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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.