Holomorphic subordinated semigroups

Adel Saddi

Commentationes Mathematicae Universitatis Carolinae (2002)

  • Volume: 43, Issue: 3, page 457-466
  • ISSN: 0010-2628

Abstract

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If ( e - t A ) t > 0 is a strongly continuous and contractive semigroup on a complex Banach space B , then - ( - A ) α , 0 < α < 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 ∈ H , the operator - f ( - A ) generates a holomorphic semigroup.

How to cite

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Saddi, Adel. "Holomorphic subordinated semigroups." Commentationes Mathematicae Universitatis Carolinae 43.3 (2002): 457-466. <http://eudml.org/doc/248978>.

@article{Saddi2002,
abstract = {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.},
author = {Saddi, Adel},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {holomorphic semigroup; Bernstein function; holomorphic semigroup; Bernstein function},
language = {eng},
number = {3},
pages = {457-466},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Holomorphic subordinated semigroups},
url = {http://eudml.org/doc/248978},
volume = {43},
year = {2002},
}

TY - JOUR
AU - Saddi, Adel
TI - Holomorphic subordinated semigroups
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2002
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 43
IS - 3
SP - 457
EP - 466
AB - 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.
LA - eng
KW - holomorphic semigroup; Bernstein function; holomorphic semigroup; Bernstein function
UR - http://eudml.org/doc/248978
ER -

References

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  1. Carasso A., Kato T., On subordinated holomorphic semigroups, Trans. Amer. Math. Soc. 327 2 (1991), 867-878. (1991) Zbl0743.47017MR1018572
  2. Berg C., Forst G., Potential Theory on Locally Compact Abelian Groups, Springer Verlag, Ergebnisse der Mathematics, vol. 87, 1975. Zbl0308.31001MR0481057
  3. Hirsch F., Domaines d'opérateurs représentés comme intégrales de résolvantes, J. Funct. Anal. 23 3 (1976), 199-217. (1976) Zbl0341.47013MR0428105
  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. (1996) Zbl0923.47023MR1380710
  5. Lumer G., Paquet L., Semi-groupes holomorphes et équations d'évolution, C.R. Acad. Sci. Paris Série A 284 (1977), 237-240. (1977) Zbl0351.35013MR0428106
  6. Paquet L., Semi-groupes holomorphes en norme sup, Séminaire de théorie du potentiel Paris, no. 4, Lecture Notes in Math. 713, 1979. 
  7. Yosida K., Functional Analysis, second edition, Springer Verlag, Berlin-Heidelberg-New York, 1968. MR0239384

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