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Construction of polynomials on a number of pseudoconvex domains

Published online by Cambridge University Press:  26 February 2010

Satoru Watari
Satoru Watari
Affiliation:
Nihon University, 8–14, Kanda Surugadai, 1-chōme, Chiyoda-ku, Tokyo, 101, Japan.
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Extract

The purpose of this paper is to construct polynomials on ℂn which can approximate to the product of two holomorphic functions defined on a neighbourhood of any boundary point of a number of pseudoconvex domains in ℂn (called the “H-pseudoconvex domain”). It should be noted that we have only mentioned that the same conclusion holds true for a strictly pseudoconvex domain in the sense of Levi in [3, p. 109]. We shall begin with the definition of H-pseudoconvexity as follows, cf [3, p. 113].

Type
Research Article
Information
Mathematika , Volume 34 , Issue 2 , December 1987 , pp. 172 - 177
Copyright
Copyright © University College London 1987

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References

1.Mir, H. EI. Fonction plurisousharmoniques et ensemble polaires. Séminaires Lelong, P.Skoda, H. (Analyse) Année 1978-79. Led. Notes in Math., 822 (1980), 61–76.Google Scholar
2.Josefson, B.. On the equivalence between locally polar and globally polar sets for plurisubharmonic functions on Cn. Arkiv för Mat., 16 (1978), 109–115.CrossRefGoogle Scholar
3.Kranz, S. G.. Function theory of several complex variables (John Wiley, 1982).Google Scholar