Displaying similar documents to “Vector-valued holomorphic and harmonic functions”

Extension of vector-valued holomorphic and harmonic functions

José Bonet, Leonhard Frerick, Enrique Jordá (2007)

Studia Mathematica

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We present a unified approach to the study of extensions of vector-valued holomorphic or harmonic functions based on the existence of weak or weak*-holomorphic or harmonic extensions. Several recent results due to Arendt, Nikolski, Bierstedt, Holtmanns and Grosse-Erdmann are extended. An open problem by Grosse-Erdmann is solved in the negative. Using the extension results we prove existence of Wolff type representations for the duals of certain function spaces.

Bounded holomorphic functions with multiple sheeted pluripolar hulls

Armen Edigarian, Józef Siciak, Włodzimierz Zwonek (2006)

Studia Mathematica

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We describe compact subsets K of ∂𝔻 and ℝ admitting holomorphic functions f with the domains of existence equal to ℂ∖K and such that the pluripolar hulls of their graphs are infinitely sheeted. The paper is motivated by a recent paper of Poletsky and Wiegerinck.

Integral holomorphic functions

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.

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.