The Hille-Yosida theorem for resolvent operators of multiparameter semigroups - Lavrent'ev, A. S.; Mishura, Yu. S. (Ukrains’kyi Matematychnyi Zhurnal, 1996)
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.