Displaying similar documents to “Operator representations of definitizable functions.”

A parabolic Pommerenke-Levin-Yoccoz inequality

Xavier Buff, Adam L. Epstein (2002)

Fundamenta Mathematicae

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In a recent preprint [B], Bergweiler relates the number of critical points contained in the immediate basin of a multiple fixed point β of a rational map f: ℙ¹ → ℙ¹, the number N of attracting petals and the residue ι(f,β) of the 1-form dz/(z-f(z)) at β. In this article, we present a different approach to the same problem, which we were developing independently at the same time. We apply our method to answer a question raised by Bergweiler. In particular, we prove that when there...

Complex geodesics and isometries in Cartan domains of type four

Edoardo Vesentini (1995)

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

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Holomorphic maps of Cartan domains of type four preserving the supports of complex geodesics are characterized, providing, in particular, a new description of holomorphic isometries.

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.

Spectral properties of a certain class of Carleman operators

S. M. Bahri (2007)

Archivum Mathematicum

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The object of the present work is to construct all the generalized spectral functions of a certain class of Carleman operators in the Hilbert space L 2 X , μ and establish the corresponding expansion theorems, when the deficiency indices are (1,1). This is done by constructing the generalized resolvents of A and then using the Stieltjes inversion formula.