The Hille-Yosida theorem for resolvent operators of multiparameter semigroups

Abstract

We consider multiparameter semigroups of two types (multiplicative and coordinatewise) and resolvent operators associated with such semigroups. We prove an alternative version of the Hille-Yosida theorem in terms of resolvent operators. For simplicity of presentation, we give statements and proofs for two-parameter semigroups.