| 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:
|
http://hdl.handle.net/10338.dmlcz/119334 |
| . |
| 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 |
| . |
