Equilibrium Distributions and Degree of Rational Approximation of Analytic Functions

A theorem is proved on the degree of rational approximation of sequences of analytic functions given by Cauchy-type integrals of the form The theorem is formulated in terms connected with the equilibrium distribution of the charge on the plates of a capacitor under the assumption that an external field acts on the plate , and this plate satisfies a certain symmetry condition in the field . The theorem is used to solve the problem of the degree of rational approximation of the function on . Bibliography: 44 titles.