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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
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
Citation:
A. S. Sadullaev, “On Analytic Multifunctions”, Mat. Zametki, 83:5 (2008), 715–721; Math. Notes, 83:5 (2008), 652–656
Linking options:
https://www.mathnet.ru/eng/mzm4136https://doi.org/10.4213/mzm4136 https://www.mathnet.ru/eng/mzm/v83/i5/p715
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Abstract page: | 409 | Full-text PDF : | 190 | References: | 34 | First page: | 7 |
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