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Mat. Sb., 2005, Volume 196, Number 5, Pages 145–156 (Mi msb1361)  

This article is cited in 1 scientific paper (total in 1 paper)

Pluriharmonic continuation in a fixed direction

A. S. Sadullaev

Al-Kharezmi Urgench State University, Khorezm, Uzbekistan

Abstract: Questions of the holomorphic and the pluriharmonic continuation of functions in a fixed direction are considered. It is shown that in the continuation of pluriharmonic functions from a boundary system of lines one usually confronts many-valued extensions. This phenomenon is directly related to a counterexample of Levenberg and Slodkowski demonstrating that there exists no potential for a pseudoconvex set in the general case.

DOI: https://doi.org/10.4213/sm1361

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English version:
Sbornik: Mathematics, 2005, 196:5, 765–775

Bibliographic databases:

UDC: 517.55+517.519
MSC: Primary 32Dxx; Secondary 32U15
Received: 07.06.2004

Citation: A. S. Sadullaev, “Pluriharmonic continuation in a fixed direction”, Mat. Sb., 196:5 (2005), 145–156; Sb. Math., 196:5 (2005), 765–775

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. S. Sadullaev, S. A. Imomkulov, “Extension of Holomorphic and Pluriharmonic Functions with Thin Singularities on Parallel Sections”, Proc. Steklov Inst. Math., 253 (2006), 144–159  mathnet  crossref  mathscinet
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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