The Lumer-Phillips Theorem For Two--parameter C0--semigroups

Abstract

In this paper we extend the Lumer-Phillips theorem to the context of two--parameter C0-semigroup of contractions. That is, we characterize the infinitesimal generators of two--parameter C0-semigroups of contractions. Conditions on the behavior of the resolvent of operators, which are necessary and sufficient for the pair of operators to be the infinitesimal generator of a C0-semigroup of contractions are given.

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