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Functional Calculus for Infinitesimal Generators of Holomorphic Semigroups

✍ Scribed by José E. Galé; Tadeusz Pytlik

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
523 KB
Volume
150
Category
Article
ISSN
0022-1236

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✦ Synopsis

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 in L 1 (R n ) and L 1 (G), for a stratified Lie group G. We give also a self-contained theory of smooth absolutely continuous functions on the half line [0, ).

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