Variation of the equilibrium energy and the S-property of stationary compact sets

This paper studies a variation of the equilibrium energy for a certain fairly general functional which appears naturally in the solution of many rational approximation problems of multi-valued analytic functions. The main result of this work states that for the energy functional under consideration and a certain class of admissible compact sets, related to the function to be approximated, the corresponding stationary compact set is fully characterized by the so-called S-property. Bibliography: 38 titles.

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