Observatorio de Investigación y Desarrollo Tecnológico


  • QUAESTIONES MATHEMATICAE

    Volumen: 1, Numero: 1, Páginas: [14]p.

    ON THE CONTINUITY OF THE ADJOINT OF EVOLUTION OPERATORS

    Abstract

    By associating a quasi semigroup to a commutative evolution operator and using techniques from vector measures like the Gel?fand integral and the Radon-Nikodym theorem for Bochner integral, we prove the continuity on [0, ?) of the adjoint of a certain class of evolution operators. Furthermore, we provide examples of evolution operators satisfying our conclusion. We also provide an application to optimal control theory; particularly, to an optimal control problem governed by a time-varying heat equation


    Keywords


    Gel?fand integral, adjoint of evolution operators, Asplund spaces, strongly continuous semigroups


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