Regular and limit sets for holomorphic correspondences

S. Bullett; C. Penrose

Displaying similar documents to “Regular and limit sets for holomorphic correspondences”

Holomorphic series expansion of functions of Carleman type

Taib Belghiti (2004)

Annales Polonici Mathematici

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Let f be a holomorphic function of Carleman type in a bounded convex domain D of the plane. We show that f can be expanded in a series f = ∑ₙfₙ, where fₙ is a holomorphic function in Dₙ satisfying $s u p_{z \in D ₙ} | f ₙ (z) | \leq C ϱ ⁿ$ for some constants C > 0 and 0 < ϱ < 1, and where (Dₙ)ₙ is a suitably chosen sequence of decreasing neighborhoods of the closure of D. Conversely, if f admits such an expansion then f is of Carleman type. The decrease of the sequence Dₙ characterizes the smoothness of f. ...

Variations of complex structures on an open Riemann surface

M. S. Narasimhan (1961)

Annales de l'institut Fourier

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Soit $U_{1}$ un ouvert dans $C^{m}$ . Soit $π_{1} : S \to U_{1}$ une famille holomorphe de structures complexes sur une surface de Riemann non-compacte $M$ , avec $S_{t_{0}} = π_{1}^{- 1} (t_{0}) = M$ . ( $S = S (M \times U_{1})$ est une structure complexe sur le produit différentiable $M \times U_{1}$ ). Soit $M_{1}$ un domaine relativement compact dans $M$ . On démontre : pour tout voisinage de Stein $U$ de $t_{0}$ , assez petit, la famille $π_{1} : S (M_{1} \times U) \to U$ est isomorphe à la famille $π : Ω \to π (Ω)$ , où $Ω$ est un de la variété produit $M \times C^{m}$ , $π$ étant la projection $M \times C^{m} \to C^{m}$ . On donne aussi un résultat analogue pour le cas des variations différentiables. ...

Extension of separately holomorphic functions-a survey 1899-2001

Peter Pflug (2003)

Annales Polonici Mathematici

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This note is an attempt to describe a part of the historical development of the research on separately holomorphic functions.

On some properties of a differential operator on the polydisk.

Shamoyan, Romi, Li, Songxiao (2008)

Banach Journal of Mathematical Analysis [electronic only]

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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...

L-holomorphic functions

M. Nikić (1986)

Matematički Vesnik

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Extensions of holomorphic motions

Zbigniew Slodkowski (1995)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Intermediate holomorphy

M. Nikić (1988)

Matematički Vesnik

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Extension of separately holomorphic functions defined in non-open sets in the infinite dimensional case

Ludwik M. Drużkowski (1983)

Annales Polonici Mathematici

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On Some Correspondence between Holomorphic Functions in the Unit Disc and Holomorphic Functions in the Left Halfplane

Ewa Ligocka (2009)

Bulletin of the Polish Academy of Sciences. Mathematics

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We study a correspondence L between some classes of functions holomorphic in the unit disc and functions holomorphic in the left halfplane. This correspondence is such that for every f and w ∈ ℍ, exp(L(f)(w)) = f(expw). In particular, we prove that the famous class S of univalent functions on the unit disc is homeomorphic via L to the class S(ℍ) of all univalent functions g on ℍ for which g(w+2πi) = g(w) + 2πi and $l i m_{R e z \to - \infty} (g (w) - w) = 0$ .

The image of a finely holomorphic map is pluripolar

Armen Edigarian, Said El Marzguioui, Jan Wiegerinck (2010)

Annales Polonici Mathematici

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We prove that the image of a finely holomorphic map on a fine domain in ℂ is a pluripolar subset of ℂⁿ. We also discuss the relationship between pluripolar hulls and finely holomorphic functions.

A method of holomorphic retractions and pseudoinverse matrices in the theory of continuation of δ-tempered functions

Marek Jarnicki

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CONTENTS§1. Introduction.................................................................................................................5§2. Basic properties of δ-tempered holomorphic functions...............................................8§3. Holomorphic continuation and holomorphic retractions.............................................20§4. Continuation from regular neighbourhoods...............................................................32§5. Continuation from δ-regular submanifolds;...

A boundary cross theorem for separately holomorphic functions

Peter Pflug, Viêt-Anh Nguyên (2004)

Annales Polonici Mathematici

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Let D ⊂ ℂⁿ and $G \subset ℂ^{m}$ be pseudoconvex domains, let A (resp. B) be an open subset of the boundary ∂D (resp. ∂G) and let X be the 2-fold cross ((D∪A)×B)∪(A×(B∪G)). Suppose in addition that the domain D (resp. G) is locally ² smooth on A (resp. B). We shall determine the “envelope of holomorphy” X̂ of X in the sense that any function continuous on X and separately holomorphic on (A×G)∪(D×B) extends to a function continuous on X̂ and holomorphic on the interior of X̂. A generalization of this...

A generalization of the Malgrange-Zerner theorem

Ludwik M. Drużkowski (1980)

Annales Polonici Mathematici

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The holomorphic contractibility of two generalized Teichmüller spaces.

Earle, Clifford J. (2004)

Publications de l'Institut Mathématique. Nouvelle Série

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