The complex inversion formula in UMD spaces for families of bounded operators |
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| Authors: | Carlos Lizama Julio Cesar de Souza |
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| Affiliation: | 1. Departamento de Matemática, Facultad de Ciencias , Universidad de Santiago de Chile , Casilla 307-Correo 2, Santiago , Chile carlos.lizama@usach.cl;3. Departamento de Matemática , Universidade Federal de Pernambuco , Av. Prof. Luiz Freire, S/N, Recife-PE , CEP 50540-740 , Brazil |
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| Abstract: | In this article, we prove that in UMD Banach spaces the complex inversion formula of the Laplace transform is valid, in the strong sense, for wide classes of families of bounded linear operators. Our approach allows us to recover (in a unified way) known results about C 0-semigroups, cosine functions and resolvent families as well as to prove new results for k-convoluted semigroups and integrated semigroups, among others. |
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| Keywords: | UMD spaces complex inversion of Laplace transform k-convoluted semigroups |
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