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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Invariance of the $ L$-regularity of compact sets in $ {\bf C}\sp{N}$ under holomorphic mappings

Author: W. Pleśniak
Journal: Trans. Amer. Math. Soc. 246 (1978), 373-383
MSC: Primary 32E30; Secondary 32E20
MathSciNet review: 515544
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Abstract: The property for a polynomially convex compact set E in $ {C^N}$ that the Siciak extremal function $ {\Phi _E}$ be continuous or, equivalently, that E satisfy some Bernstein type inequality, is proved to be invariant under a large class of holomorphic mappings with values in $ {C^M}(M \leqslant N)$ including all open holomorphic mappings. Local specifications of this result are also given.

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Keywords: Extremal function, Green function, approximation of analytic functions, polynomials, Bernstein inequality
Article copyright: © Copyright 1978 American Mathematical Society