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Title: Holomorphic subordinated semigroups (English)
Author: Saddi, Adel
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 43
Issue: 3
Year: 2002
Pages: 457-466
Category: math
Summary: If $(e^{-tA})_{t>0}$ is a strongly continuous and contractive semigroup on a complex Banach space $B$, then $-(-A)^\alpha $, $0<\alpha <1$, generates a holomorphic semigroup on $B$. This was proved by K. Yosida in [7]. Using similar techniques, we present a class $H$ of Bernstein functions such that for all $f\in H$, the operator $-f(-A)$ generates a holomorphic semigroup. (English)
Keyword: holomorphic semigroup
Keyword: Bernstein function
MSC: 35B40
MSC: 35B65
MSC: 35K65
MSC: 47A60
MSC: 47D06
idZBL: Zbl 1090.35109
idMR: MR1920520
Date available: 2009-01-08T19:23:46Z
Last updated: 2012-04-30
Stable URL:
Reference: [1] Carasso A., Kato T.: On subordinated holomorphic semigroups.Trans. Amer. Math. Soc. 327 2 (1991), 867-878. Zbl 0743.47017, MR 1018572
Reference: [2] Berg C., Forst G.: Potential Theory on Locally Compact Abelian Groups.Springer Verlag, Ergebnisse der Mathematics, vol. 87, 1975. Zbl 0308.31001, MR 0481057
Reference: [3] Hirsch F.: Domaines d'opérateurs représentés comme intégrales de résolvantes.J. Funct. Anal. 23 3 (1976), 199-217. Zbl 0341.47013, MR 0428105
Reference: [4] Jacob N., Schilling R.L.: Subordination in the sense of S. Bochner: An approach through pseudo differential operators.Math. Nachr. 178 (1996), 199-231. Zbl 0923.47023, MR 1380710
Reference: [5] Lumer G., Paquet L.: Semi-groupes holomorphes et équations d'évolution.C.R. Acad. Sci. Paris Série A 284 (1977), 237-240. Zbl 0351.35013, MR 0428106
Reference: [6] Paquet L.: Semi-groupes holomorphes en norme sup.Séminaire de théorie du potentiel Paris, no. 4, Lecture Notes in Math. 713, 1979.
Reference: [7] Yosida K.: Functional Analysis, second edition.Springer Verlag, Berlin-Heidelberg-New York, 1968. MR 0239384


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