Estimates near the origin for functional calculus on analytic semigroups

I. Chalendar; J. Esterle; J. R. Partington

Estimates near the origin for functional calculus on analytic semigroups

Functional Analysis 2018-01-12 v2 Complex Variables

Authors: I. Chalendar , J. Esterle , J. R. Partington

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.

Keywords

operator semigroups fourier analysis

Cite

@article{arxiv.1709.06777,
  title  = {Estimates near the origin for functional calculus on analytic semigroups},
  author = {I. Chalendar and J. Esterle and J. R. Partington},
  journal= {arXiv preprint arXiv:1709.06777},
  year   = {2018}
}

Comments

18 pages, 1 figure. Revised version

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