On analytic multifunctions. (English. Russian original) Zbl 1155.32300
Math. Notes 83, No. 5, 652-656 (2008); translation from Mat. Zametki 83, No. 5, 715-721 (2008).
Summary: 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 \(S_a = S \cap \{z = a\}\).
MSC:
| 32A12 | Multifunctions of several complex variables |
Keywords:
analytic multifunction; subharmonic function; pseudoconcavity; pseudoconvexity; plurisubharmonicity; pluripolarity; capacity of a set; hartogs seriesReferences:
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