Title: Weakly admissible vector equilibrium problems
Authors: Hardy, Adrien ×
Kuijlaars, Arno #
Issue Date: Jun-2012
Publisher: Academic Press
Series Title: Journal of Approximation Theory vol:164 issue:6 pages:854-868
Abstract: We establish lower semi-continuity and strict convexity of the energy functionals for a large class of vector equilibrium problems in logarithmic potential theory. This, in particular, implies the existence and uniqueness of a minimizer for such vector equilibrium problems. Our work extends earlier results in that we allow unbounded supports without having strongly confining external fields. To deal with the possible noncompactness of supports, we map the vector equilibrium problem onto the Riemann sphere and our results follow from a study of vector equilibrium problems on compacts in higher dimensions. Our results cover a number of cases that were recently considered in random matrix theory and for which the existence of a minimizer was not clearly established yet.
ISSN: 0021-9045
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Analysis Section
× corresponding author
# (joint) last author

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