Lower estimates near the origin for functional calculus on operator semigroups

Isabelle Chalendar (1) , Jean Esterle (2) , Jonathan R. Partington (3)

1 EDPA - Équations aux dérivées partielles, analyse
2 IMB - Institut de Mathématiques de Bordeaux
3 School of Mathematics

This paper provides sharp lower estimates near the origin for the functional calculus F(−uA) of a generator A of an operator semi- group defined on the (strictly) positive real line; here F is given as the Laplace transform of a measure or distribution. The results are linked to the existence of an identity element or an exhaustive sequence of idempotents 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.

Mots clés: strongly continuous semigroup; functional calculus; Laplace transform; maximum principle

Domaines: Analyse fonctionnelle [math.FA]

Isabelle Chalendar, Jean Esterle, Jonathan R. Partington. Lower estimates near the origin for functional calculus on operator semigroups. Journal of Functional Analysis, 2015, 269 (06), pp.1620-1635. ⟨hal-00959785⟩