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Mat. Zametki, 2008, Volume 83, Issue 5, Pages 715–721 (Mi mz4136)  

This article is cited in 3 scientific papers (total in 3 papers)

On Analytic Multifunctions

A. S. Sadullaev

Al-Kharezmi Urgench State University, Khorezm, Uzbekistan

Abstract: For any multifunction $S\subset D_z\times\mathbb{C}_w$, we give a criterion for analyticity (pseudoconcavity) in terms of plurisubharmonicity of the function $V(z,w)=-\ln\rho(w,S_z)$, where $\rho(w,S_a)$ stands for the distance from the point $w$ to the set $S_a=S\capż=a\}$.

Keywords: analytic multifunction, subharmonic function, pseudoconcavity, pseudoconvexity, plurisubharmonicity, pluripolarity, capacity of a set, Hartogs series

DOI: https://doi.org/10.4213/mzm4136

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English version:
Mathematical Notes, 2008, 83:5, 652–656

Bibliographic databases:

UDC: 517.55
Received: 26.03.2007
Revised: 14.01.2008

Citation: A. S. Sadullaev, “On Analytic Multifunctions”, Mat. Zametki, 83:5 (2008), 715–721; Math. Notes, 83:5 (2008), 652–656

Citation in format AMSBIB
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\paper On Analytic Multifunctions
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\pages 715--721
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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. Azimbaj S. Sadullaev, “Some Problems in the Theory of Analytic Multifunctions”, Zhurn. SFU. Ser. Matem. i fiz., 1:4 (2008), 432–434  mathnet  elib
    2. Aytuna A., Sadullaev A., “Parabolic Stein Manifolds”, Math. Scand., 114:1 (2014), 86–109  crossref  mathscinet  zmath  isi  scopus
    3. Aytuna A., Sadullaev A., “Polynomials on parabolic manifolds”, Topics in Several Complex Variables, Contemporary Mathematics, 662, eds. Ibragimov Z., Levenberg N., Pinchuk S., Sadullaev A., Amer Mathematical Soc, 2016, 1–22  crossref  mathscinet  zmath  isi
  • Математические заметки Mathematical Notes
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