Holomorphic solutions to linear first-order functional differential equations.

In finite-dimensional complex analysis, the extension of holomorphic maps has been investigated by many authors. In recent years some authors have considered this problem in the infinite-dimensional case. The aim of the present note is to study the extension of holomorphic maps with values in some Banach complex manifolds.

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 a holomorphic solution of a singular partial differential equation with many simple poles

Joji Kajiwara (1974)

Czechoslovak Mathematical Journal

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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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Intermediate holomorphy

M. Nikić (1988)

Matematički Vesnik

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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.

A generalization of the Malgrange-Zerner theorem

Ludwik M. Drużkowski (1980)

Annales Polonici Mathematici

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