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The Hille-Yosida theorem for resolvent operators of multiparameter semigroups

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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.

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Authors
  1. Yu. S. Mishura
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  2. A. S. Lavrent’ev
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Mishura, Y.S., Lavrent’ev, A.S. The Hille-Yosida theorem for resolvent operators of multiparameter semigroups. Ukr Math J 48, 65–74 (1996). https://doi.org/10.1007/BF02390984

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  • DOI: https://doi.org/10.1007/BF02390984

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