Holomorphic semigroups of holomorphic isometries

Edoardo Vesentini

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1988)

  • Volume: 82, Issue: 1, page 43-49
  • ISSN: 1120-6330

Abstract

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A previous paper was devoted to the construction of non-trivial holomorphic families of holomorphic isometries for the Carathéodory metric of a bounded domain in a complex Banach space, fixing a point in the domain. The present article shows that such a family cannot exist if it contains a strongly continuous one parameter semigroup.

How to cite

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Vesentini, Edoardo. "Holomorphic semigroups of holomorphic isometries." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 82.1 (1988): 43-49. <http://eudml.org/doc/287230>.

@article{Vesentini1988,
abstract = {A previous paper was devoted to the construction of non-trivial holomorphic families of holomorphic isometries for the Carathéodory metric of a bounded domain in a complex Banach space, fixing a point in the domain. The present article shows that such a family cannot exist if it contains a strongly continuous one parameter semigroup.},
author = {Vesentini, Edoardo},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Carathéodory and Kobayashi metrics; Holomorphic isometries; holomorphic semigroups of holomorphic isometries; strongly continuous one parameter semigroup},
language = {eng},
month = {3},
number = {1},
pages = {43-49},
publisher = {Accademia Nazionale dei Lincei},
title = {Holomorphic semigroups of holomorphic isometries},
url = {http://eudml.org/doc/287230},
volume = {82},
year = {1988},
}

TY - JOUR
AU - Vesentini, Edoardo
TI - Holomorphic semigroups of holomorphic isometries
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1988/3//
PB - Accademia Nazionale dei Lincei
VL - 82
IS - 1
SP - 43
EP - 49
AB - A previous paper was devoted to the construction of non-trivial holomorphic families of holomorphic isometries for the Carathéodory metric of a bounded domain in a complex Banach space, fixing a point in the domain. The present article shows that such a family cannot exist if it contains a strongly continuous one parameter semigroup.
LA - eng
KW - Carathéodory and Kobayashi metrics; Holomorphic isometries; holomorphic semigroups of holomorphic isometries; strongly continuous one parameter semigroup
UR - http://eudml.org/doc/287230
ER -

References

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  1. DINEEN, S., TIMONEY, R.M. and VIGUÈ, J.-P. (1985) - Pseudodistances invariantes sur les domaines d'un espace localement convexe, «Ann. Scuola Norm. Sup. Pisa», (4) 12, 515-529. Zbl0603.46052MR848840
  2. FRANZONI, T. and VESENTINI, E. (1980) - Holomorphic maps and invariant distances, North-Holland, Amsterdam-New York-Oxford, 1985. Zbl0447.46040MR563329
  3. GREINER, G. and NAGEL, R. (1986) - Spectral theory of semigroups on Banach spaces, in R. NAGEL (Editor), One-parameter semi groups of positive operators, Lecture Notes in Mathematics, n. 1184, Springer-Verlag, Berlin-Heidelberg-New York-Tokyo, 60-97. Zbl0585.47030
  4. HARRIS, L.A. (1979) - Schwarz-Pick systems of pseudometrics for domains in normed linear spaces, in J.A. BARROSO (Editor), Advances in holomorphy, North-Holland, Amsterdam-New York-Oxford, 354-406. Zbl0409.46053MR520667
  5. HILLE, E. and PHILLIPS, R.S. (1957) - Functional analysis and semigroups, «Amer. Math. Soc. Colloquium Publ.», 31, «Amer. Math. Soc.», Providence, R.I. Zbl0078.10004MR89373
  6. PAZY, A. (1983) - Semigroups of linear operators and applications to partial differential equations, Springer-Verlag, New York-Berlin-Heidelberg-Tokyo. Zbl0516.47023MR710486DOI10.1007/978-1-4612-5561-1
  7. REIFFEN, H.-J. (1965) - Die Carathéodorysche Distanz und ihre zugehörige Dijferentialmetrik, «Math. Annalen», 161, 315-324. Zbl0141.08803MR196133
  8. VESENTINI, E. (1982) - Complex geodesies and holomorphic maps, «Symposia Mathematica», 26, 211-230. Zbl0506.32008MR663034
  9. VESENTINI, E. (1987) - Holomorphic families of holomorphic isometries, in C.A. BERENSTEIN (Editor), Complex Analysis III, Lecture Notes in Mathematics, n. 1277, Springer-Verlag, Berlin-Heidelberg-New York-London-Paris-Tokyo, 290-302. Zbl0643.32009MR922341DOI10.1007/BFb0078252

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