Direct integrals of strongly continuous operator semigroups

2019/12/06 by Ng, Abraham C. S.
#(47D07) #34K30 #35B40 #47D06 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1912.03084

Abstract

The goal of this article is to develop a theory for direct integrals of C₀-semigroups on Hilbert spaces parallel to the recent approach by Lachowicz and Moszyński for direct sums of Banach spaces, diagonal operators, and semigroups. In it we deal with the existence and characterisation of semigroups, asymptotic rates, and questions of decomposability.

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