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.
John Wermer (1985)
Annales Polonici Mathematici
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Angus E. Taylor (1937)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Zbigniew Slodkowski (1986)
Rendiconti del Seminario Matematico della Università di Padova
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C. Denson Hill, Geraldine Taiani (1978)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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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.
Mohamed S. Baouendi (1981)
Journées équations aux dérivées partielles
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P. Tworzewski, T. Winiarski (1983)
Annales Polonici Mathematici
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Guillaume Valette (2005)
Annales Polonici Mathematici
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We give criteria of finite determinacy for the volume and multiplicities. Given an analytic set described by {v = 0}, we prove that the log-analytic expansion of the volume of the intersection of the set and a "little ball" is determined by that of the set defined by the Taylor expansion of v up to a certain order if the mapping v has an isolated singularity at the origin. We also compare the cardinalities of finite fibers of projections restricted to such a set.
Herwig Hauser, Gerd Müller (1990)
Compositio Mathematica
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Grzegorz Łysik (2000)
Annales Polonici Mathematici
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Definitions, properties, examples and applications of generalized analytic functions introduced by B. Ziemian are presented.