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On Some Functions That Send Each Generator of a C0-Semigroup to the Generator of a Holomorphic Semigroup

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Abstract

We give some conditions on functions of the Schoenberg class T for them to send the generators of uniformly bounded semigroup of class C 0 to the generators of holomorphic semigroups. This generalizes Yosida, Balakrishnan, and Kato's result relating to fractional powers of operators. The functional calculus of generators of C 0-semigroups which uses the class T was constructed in the preceding articles of the author.

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  1. Skorina Gomel' State University, Russia

    A. R. Mirotin

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  1. A. R. Mirotin
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Mirotin, A.R. On Some Functions That Send Each Generator of a C0-Semigroup to the Generator of a Holomorphic Semigroup. Siberian Mathematical Journal 43, 114–123 (2002). https://doi.org/10.1023/A:1013832806887

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  • DOI: https://doi.org/10.1023/A:1013832806887

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