Lineability of the set of holomorphic mappings with dense range

Jerónimo López-Salazar

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Displaying similar documents to “Lineability of the set of holomorphic mappings with dense range”

Proper holomorphic self-mappings of the symmetrized bidisc

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Annales Polonici Mathematici

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We characterize proper holomorphic self-mappings 𝔾₂ → 𝔾₂ for the symmetrized bidisc 𝔾₂ = {(λ₁+λ₂,λ₁λ₂): |λ₁|,|λ₂| < 1} ⊂ ℂ².

The theorem of Forelli for holomorphic mappings into complex spaces

Pham Ngoc Mai, Do Duc Thai, Le Tai Thu (2004)

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Generalizations of the theorem of Forelli to holomorphic mappings into complex spaces are given.

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Viêt-Anh Nguyên (2009)

Colloquium Mathematicae

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We describe a part of the recent developments in the theory of separately holomorphic mappings between complex analytic spaces. Our description focuses on works using the technique of holomorphic discs.

The Łojasiewicz exponent of c-holomorphic mappings

Maciej P. Denkowski (2005)

Annales Polonici Mathematici

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The aim of this paper is to study the Łojasiewicz exponent of c-holomorphic mappings. After introducing an order of flatness for c-holomorphic mappings we give an estimate of the Łojasiewicz exponent in the case of isolated zero, which is a generalization of the one given by Płoski and earlier by Chądzyński for two variables.

A uniqueness theorem of Cartan-Gutzmer type for holomorphic mappings in ℂⁿ

Piotr Liczberski, Jerzy Połubiński (2002)

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We continue our previous work on a problem of Janiec connected with a uniqueness theorem, of Cartan-Gutzmer type, for holomorphic mappings in ℂⁿ. To solve this problem we apply properties of (j;k)-symmetrical functions.

Fixed points of holomorphic mappings for domains in Banach spaces.

Harris, Lawrence A. (2003)

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Colloquium Mathematicae

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We study a linearization of a real-analytic plane map in the neighborhood of its fixed point of holomorphic type. We prove a generalization of the classical Koenig theorem. To do that, we use the well known results concerning the local dynamics of holomorphic mappings in ℂ².

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.

A note on the Nullstellensatz for c-holomorphic functions

Maciej P. Denkowski (2007)

Annales Polonici Mathematici

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We begin this article with a graph theorem and a kind of Nullstellensatz for weakly holomorphic functions. This yields a general Nullstellensatz for c-holomorphic functions on locally irreducible sets. In Section 2 some methods of Płoski-Tworzewski permit us to prove an effective Nullstellensatz for c-holomorphic functions in the case of a proper intersection with the degree of the intersection cycle as exponent. We also extend this result to the case of isolated improper intersection,...

Lineability and algebrability of the set of holomorphic functions with a given domain of existence

Thiago R. Alves (2014)

Studia Mathematica

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We show that if U is a domain of existence in a separable Banach space, then the set of holomorphic functions on U whose domain of existence is U is lineable and algebrable.

The range of vector valued holomorphic mappings

Richard M. Aron (1976)

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On some properties of a differential operator on the polydisk.

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Banach Journal of Mathematical Analysis [electronic only]

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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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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.

Extending proper holomorphic mappings of positive codimension.

Franc Forstneric (1989)

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Intermediate holomorphy

M. Nikić (1988)

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A Hahn-Banach Theorem for Holomorphic Mappings on Locally Convex Spaces.

Ralf Hollstein (1984/85)

Mathematische Zeitschrift

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A generalization of the Malgrange-Zerner theorem

Ludwik M. Drużkowski (1980)

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Verónica Dimant, Pablo Galindo, Manuel Maestre, Ignacio Zalduendo (2004)

Studia Mathematica

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We define the class of integral holomorphic functions over Banach spaces; these are functions admitting an integral representation akin to the Cauchy integral formula, and are related to integral polynomials. After studying various properties of these functions, Banach and Fréchet spaces of integral holomorphic functions are defined, and several aspects investigated: duality, Taylor series approximation, biduality and reflexivity.

Holomorphic mappings between spaces of different dimensions. II.

Peichu Hu (1994)

Mathematische Zeitschrift

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Bounded projections and decompositions in spaces of holomorphic functions

M. Mateljević (1986)

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Holomorphic mappings between spaces of different dimensions. I.

Peichu Hu (1993)

Mathematische Zeitschrift

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