Jensen measures and analytic multifunctions

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5 Scopus citations

Abstract

This paper describes plurisubharmonic convexity and hulls, and also analytic multifunctions in terms of Jensen measures. In particular, this allows us to get a new proof of Słodkowski's theorem stating that multifunctions are analytic if and only if their graphs are pseudoconcave. We also show that multifunctions with plurisubharmonically convex fibers are analytic if and only if their graphs locally belong to plurisubharmonic hulls of their boundaries. In the last section we prove that minimal analytic multifunctions satisfy the maximum principle and give a criterion for the existence of holomorphic selections in the graphs of analytic multifunctions.

Original languageEnglish (US)
Pages (from-to)335-352
Number of pages18
JournalArkiv for Matematik
Volume42
Issue number2
DOIs
StatePublished - Oct 2004

ASJC Scopus subject areas

  • Mathematics(all)

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