Angular limits and derivatives for holomorphic maps of infinite dimensional bounded homogeneous domains

Kazimierz Włodarczyk

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1994)

  • Volume: 5, Issue: 1, page 43-53
  • ISSN: 1120-6330

Abstract

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An infinite dimensional extension of the Pick-Julia theorem is used to derive the conditions of Carathéodory type which guarantee the existence of angular limits and angular derivatives for holomorphic maps of infinite dimensional bounded symmetric homogeneous domains in J * -algebras and in complex Hilbert spaces. The case of operator-valued analytic maps is considered and examples are given.

How to cite

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Włodarczyk, Kazimierz. "Angular limits and derivatives for holomorphic maps of infinite dimensional bounded homogeneous domains." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 5.1 (1994): 43-53. <http://eudml.org/doc/244214>.

@article{Włodarczyk1994,
abstract = {An infinite dimensional extension of the Pick-Julia theorem is used to derive the conditions of Carathéodory type which guarantee the existence of angular limits and angular derivatives for holomorphic maps of infinite dimensional bounded symmetric homogeneous domains in \( J^\{*\} \)-algebras and in complex Hilbert spaces. The case of operator-valued analytic maps is considered and examples are given.},
author = {Włodarczyk, Kazimierz},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Infinite dimensional bounded symmetric homogeneous domain; Holomorphic map; Operator-valued analytic map; Angular derivative; $ J^\{*\} $-algebra; infinite dimensional extension of the Pick-Julia theorem; conditions of Carathéodory type; existence of angular limits and angular derivatives for holomorphic maps; complex Hilbert spaces; operator-valued analytic maps; infinite dimensional bounded symmetric homogeneous domains in -algebras},
language = {eng},
month = {3},
number = {1},
pages = {43-53},
publisher = {Accademia Nazionale dei Lincei},
title = {Angular limits and derivatives for holomorphic maps of infinite dimensional bounded homogeneous domains},
url = {http://eudml.org/doc/244214},
volume = {5},
year = {1994},
}

TY - JOUR
AU - Włodarczyk, Kazimierz
TI - Angular limits and derivatives for holomorphic maps of infinite dimensional bounded homogeneous domains
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1994/3//
PB - Accademia Nazionale dei Lincei
VL - 5
IS - 1
SP - 43
EP - 53
AB - An infinite dimensional extension of the Pick-Julia theorem is used to derive the conditions of Carathéodory type which guarantee the existence of angular limits and angular derivatives for holomorphic maps of infinite dimensional bounded symmetric homogeneous domains in \( J^{*} \)-algebras and in complex Hilbert spaces. The case of operator-valued analytic maps is considered and examples are given.
LA - eng
KW - Infinite dimensional bounded symmetric homogeneous domain; Holomorphic map; Operator-valued analytic map; Angular derivative; $ J^{*} $-algebra; infinite dimensional extension of the Pick-Julia theorem; conditions of Carathéodory type; existence of angular limits and angular derivatives for holomorphic maps; complex Hilbert spaces; operator-valued analytic maps; infinite dimensional bounded symmetric homogeneous domains in -algebras
UR - http://eudml.org/doc/244214
ER -

References

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