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Differential and Analytical Properties of Semigroups of Operators

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Abstract

We systematically analyze differential and analytical properties of various kinds of semigroups of linear operators, including (local) convoluted C-semigroups and ultradistribution semigroups. The study of differentiable integrated semigroups leans heavily on the unification of the approaches of Barbu (Ann Scuola Norm Sup Pisa 23:413–429, 1969) and Pazy (Semigroups of linear operators and applications to partial differential equations. Springer, Berlin, 1983). We furnish illustrative examples of operators which generate differentiable integrated semigroups, further analyze the analytic properties of solutions of the backwards heat equation, and prove that several introduced classes of differentiable semigroups persist under bounded ‘commuting’ perturbations.

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  1. University of Novi Sad, Faculty of Technical Sciences, Trg Dositeja Obradovića 6, 21125, Novi Sad, Serbia

    Marko Kostić

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This research was supported by grant 144016 of Ministry of Science and Technological Development, Republic of Serbia.

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Kostić, M. Differential and Analytical Properties of Semigroups of Operators. Integr. Equ. Oper. Theory 67, 499–557 (2010). https://doi.org/10.1007/s00020-010-1797-4

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