### The Łojasiewicz exponent of an analytic mapping of two complex variables at an isolated zero

Jacek Chadzyński, Tadeusz Krasiński (1988)

Banach Center Publications

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Jacek Chadzyński, Tadeusz Krasiński (1988)

Banach Center Publications

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Nguyen Thanh Van (2003)

Annales Polonici Mathematici

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For functions that are separately solutions of an elliptic homogeneous PDE with constant coefficients, we prove an analogue of Siciak's theorem for separately holomorphic functions.

Sławomir Cynk (1990)

Annales Polonici Mathematici

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Jacek Stasica (2003)

Annales Polonici Mathematici

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Sufficient conditions for the existence of an analytic solution of analytic equations in the complex and real cases are given.

Mohamed S. Baouendi (1981)

Journées équations aux dérivées partielles

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Nguyen Van Dong, Nguyen Thai Son (1998)

Portugaliae Mathematica

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Tran Ngoc Giao (1992)

Annales de la Faculté des sciences de Toulouse : Mathématiques

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Maciej Klimek, Marta Kosek (2009)

Annales Polonici Mathematici

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Using a construction similar to an iterated function system, but with functions changing at each step of iteration, we provide a natural example of a continuous one-parameter family of holomorphic functions of infinitely many variables. This family is parametrized by the compact space of positive integer sequences of prescribed growth and hence it can also be viewed as a parametric description of a trivial analytic multifunction.

C. Denson Hill, Geraldine Taiani (1978)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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David E. Barrett (1983)

Mathematische Annalen

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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.

Marek Jarnicki, Peter Pflug (2011)

Colloquium Mathematicae

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We present a version of the identity principle for analytic sets, which shows that the extension theorem for separately holomorphic functions with analytic singularities follows from the case of pluripolar singularities.

Volker Aurich (1986)

Annales de l'institut Fourier

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Conditions are given which enable or disable a complex space $X$ to be mapped biholomorphically onto a bounded closed analytic subset of a Banach space. They involve on the one hand the Radon-Nikodym property and on the other hand the completeness of the Caratheodory metric of $X$.