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Matematicheskie Zametki, 2008, Volume 83, Issue 5, Pages 715–721
DOI: https://doi.org/10.4213/mzm4136 (Mi mzm4136) 		 
This article is cited in 6 scientific papers (total in 6 papers)

On Analytic Multifunctions

A. S. Sadullaev

Al-Kharezmi Urgench State University, Khorezm, Uzbekistan
Full-text PDF (438 kB) Citations (6)
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DOI: https://doi.org/10.4213/mzm4136
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 $S_a=S\cap\{z=a\}$.
Keywords: analytic multifunction, subharmonic function, pseudoconcavity, pseudoconvexity, plurisubharmonicity, pluripolarity, capacity of a set, Hartogs series.
Received: 26.03.2007
Revised: 14.01.2008
English version:
Mathematical Notes, 2008, Volume 83, Issue 5, Pages 652–656
DOI: https://doi.org/10.1134/S0001434608050088
Bibliographic databases:
UDC: 517.55
Language: Russian
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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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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