Jensen measures and analytic multifunctions

Evgeny A. Poletsky Department of Mathematics, Syracuse University

TBD mathscidoc:1701.333038

Arkiv for Matematik, 42, (2), 335-352, 2003.3
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 SÅ‚odkowski'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.
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  title={Jensen measures and analytic multifunctions},
  author={Evgeny A. Poletsky},
  booktitle={Arkiv for Matematik},
Evgeny A. Poletsky. Jensen measures and analytic multifunctions. 2003. Vol. 42. In Arkiv for Matematik. pp.335-352.
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