Sergey Pavlovich Suetin

Method of interior variations and existence of S-compact sets

The variation of equilibrium energy is analyzed for three different functionals that naturally arise in solving a number of problems in the theory of constructive rational approximation of multivalued analytic functions. The variational approach is based on the relationship between the variation of the equilibrium energy and the equilibrium measure. In all three cases the following result is obtained: for the energy functional and the class of admissible compact sets corresponding to the problem, the arising stationary compact set is fully characterized by a certain symmetry property.

Padé-Chebyshev approximants of multivalued analytic functions, variation of equilibrium energy, and the

Pade-Chebyshev approximants are considered for multivalued analytic functions that are real-valued on the unit interval . The focus is mainly on non-linear Pade-Chebyshev approximants. For such rational approximations an analogue is found of Stahls theorem on convergence in capacity of the Pade approximants in the maximal domain of holomorphy of the given function. The rate of convergence is characterized in terms of the stationary compact set for the mixed equilibrium problem of Green-logarithmic potentials. Bibliography: 79 titles.