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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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http://mi.mathnet.ru/eng/mz4136https://doi.org/10.4213/mzm4136 http://mi.mathnet.ru/eng/mz/v83/i5/p715
Citing articles on Google Scholar:
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Russian articles,
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This publication is cited in the following articles:
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Azimbaj S. Sadullaev, “Some Problems in the Theory of Analytic Multifunctions”, Zhurn. SFU. Ser. Matem. i fiz., 1:4 (2008), 432–434
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Aytuna A., Sadullaev A., “Parabolic Stein Manifolds”, Math. Scand., 114:1 (2014), 86–109
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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
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