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arXiv · 1709.06777

Estimates near the origin for functional calculus on analytic semigroups

I. Chalendar·J. Esterle·J. R. Partington
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Abstract

This paper provides sharp lower estimates near the origin for the functional calculus $F(-uA)$ of a generator $A$ of an operator semigroup defined on a sector; here $F$ is given as the Fourier--Borel transform of an analytic functional. The results are linked to the existence of an identity element in the Banach algebra generated by the semigroup. Both the quasinilpotent and non-quasinilpotent cases are considered, and sharp results are proved extending many in the literature.

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I. Chalendar, J. Esterle, J. R. Partington. 2017-09-20. Estimates near the origin for functional calculus on analytic semigroups. https://arxiv.org/abs/1709.06777

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