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Equilibrium distributions and rate of rational approximation of analytic functions. (Russian) Zbl 0645.30026

A general result is proved concerning the exact rate of best rational approximation for a large class of analytic functions. This result is stated in terms connected with equilibrium distributions in the presence of exterior fields. The proof is based on the construction of multipoint Padé approximants whose convergence properties in turn reduce to the study of limit distribution of zeros of sequences of polynomials which satisfy complex orthogonal relations with respect to varying measures. The results obtained are used to solve the well known problem concerning the rate of best rational approximation of \(e^{-x}\) on \([0,+\infty)\).

MSC:

30E10 Approximation in the complex plane
41A20 Approximation by rational functions
31A15 Potentials and capacity, harmonic measure, extremal length and related notions in two dimensions
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