The holomorphic functional calculus approach to operator semigroups

In this article we construct a holomorphic functional calculus for operators of half-plane type and show how key facts of semigroup theory (Hille-Yosida and Gomilko-Shi-Feng generation theorems, Trotter-Kato approximation theorem, Euler approximation formula, Gearhart-Priiss theorem) can be elegantl...

Teljes leírás

Elmentve itt :
Bibliográfiai részletek
Szerzők: Batty Charles
Haase Markus
Mubeen Junaid
További közreműködők: Kérchy László
Dokumentumtípus: Cikk
Megjelent: Bolyai Institute, University of Szeged Szeged 2013
Sorozat:Acta scientiarum mathematicarum 79 No. 1-2
Kulcsszavak:Szőkefalvi-Nagy Béla, Matematika, Algebra
Tárgyszavak:
Online Access:http://acta.bibl.u-szeged.hu/30875
Leíró adatok
Tartalmi kivonat:In this article we construct a holomorphic functional calculus for operators of half-plane type and show how key facts of semigroup theory (Hille-Yosida and Gomilko-Shi-Feng generation theorems, Trotter-Kato approximation theorem, Euler approximation formula, Gearhart-Priiss theorem) can be elegantly obtained in this framework. Then we discuss the notions of bounded H°°-calculus and m-bounded calculus on half-planes and their relation to weak bounded variation conditions over vertical lines for powers of the resolvent. Finally we discuss the Hilbert space case, where semigroup generation is characterised by the operator having a strong m-bounded calculus on a half-plane.
Terjedelem/Fizikai jellemzők:289-323
ISSN:0001-6969