Abstract:
A theorem is proved on the degree of rational approximation of sequences of analytic functions given by Cauchy-type integrals of the form
fn(z)=∮FΦn(t)f(t)(t−z)−1dt,z∈E.fn(z)=∮FΦn(t)f(t)(t−z)−1dt,z∈E.
The theorem is formulated in terms connected with the equilibrium distribution of the charge on the plates of a capacitor (E,F)(E,F) under the assumption that an external field φ=limn→∞(2n)−1log|Φn|−1φ=limn→∞(2n)−1log|Φn|−1 acts on the plate FF, and this plate satisfies a certain symmetry condition in the field φφ. The theorem is used to solve the problem of the degree of rational approximation of the function e−xe−x on [0,+∞)[0,+∞).
Bibliography: 44 titles.
Citation:
A. A. Gonchar, E. A. Rakhmanov, “Equilibrium distributions and degree of rational approximation of
analytic functions”, Math. USSR-Sb., 62:2 (1989), 305–348
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