Functional Calculus for Infinitesimal Generators of Holomorphic Semigroups |
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| Authors: | José E. Galé ,Tadeusz Pytlik |
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| Affiliation: | aDepartamento de Matemáticas, Facultad de Ciencias, Universidad de Zaragoza, 50009, Zaragoza, Spain;bInstytut Matematyczny, Uniwersytet Wroc?awski, pl. Grunwaldzki 2/4, 50384, Wroc?aw, Poland |
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| Abstract: | We give a functional calculus formula for infinitesimal generators of holomorphic semigroups of operators on Banach spaces, which involves the Bochner–Riesz kernels of such generators. The rate of smoothness of operating functions is related to the exponent of the growth on vertical lines of the operator norm of the semigroup. The strength of the formula is tested on Poisson and Gauss semigroups inL1(Rn) andL1(G), for a stratified Lie groupG. We give also a self-contained theory of smooth absolutely continuous functions on the half line [0, ∞). |
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| Keywords: | holomorphic semigroups functional calculus multipliers stratified Lie groups fractional derivatives Leibniz formula |
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