Rigidity of holomorphic maps and distortion of biholomorphic maps in operator Siegel domains

Kazimierz Włodarczyk

Displaying similar documents to “Rigidity of holomorphic maps and distortion of biholomorphic maps in operator Siegel domains”

The existence of angular derivatives of holomorphic maps of Siegel domains in a generalization of $C^{*}$ -algebras

Kazimierz Włodarczyk (1994)

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

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The aim of this paper is to start a systematic investigation of the existence of angular limits and angular derivatives of holomorphic maps of infinite dimensional Siegel domains in $J^{*}$ -algebras. Since $J^{*}$ -algebras are natural generalizations of $C^{*}$ -algebras, $B^{*}$ -algebras, $J C^{*}$ -algebras, ternary algebras and complex Hilbert spaces, various significant results follow. Examples are given.

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

Kazimierz Włodarczyk (1994)

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

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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.

A survey on geometric properties of holomorphic self-maps in some domains of ℂⁿ

Chiara Frosini, Fabio Vlacci (2007)

Annales Polonici Mathematici

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In this survey we give geometric interpretations of some standard results on boundary behaviour of holomorphic self-maps in the unit disc of ℂ and generalize them to holomorphic self-maps of some particular domains of ℂⁿ.

Approximation by proper holomorphic maps into convex domains

Avner Dor (1993)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Horospheres and Iterates of Holomorphic Maps.

Marco Abate (1988)

Mathematische Zeitschrift

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Non-extendable holomorphic functions

P. Pflug (1985)

Matematički Vesnik

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Proper holomorphic self-mappings of Reinhardt domains.

Yifei Pan (1991)

Mathematische Zeitschrift

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L-holomorphic functions

M. Nikić (1986)

Matematički Vesnik

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Extending holomorphic maps in infinite dimensions

Bui Dac Tac (1991)

Annales Polonici Mathematici

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Studying the sequential completeness of the space of germs of Banach-valued holomorphic functions at a points of a metric vector space some theorems on extension of holomorphic maps on Riemann domains over topological vector spaces with values in some locally convex analytic spaces are proved. Moreover, the extendability of holomorphic maps with values in complete C-spaces to the envelope of holomorphy for the class of bounded holomorphic functions is also established. These results...