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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
Minimal Discrete Energy on the Sphere
We investigate the energy of arrangements of N points on the surface of a sphere in R3, interacting through a power law potential V = rα, −2 < α < 2, where r is Euclidean distance. For α = 0, we take
Equilibrium measure and the distribution of zeros of the extremal polynomials of a discrete variable
The problem of the?limiting distribution of the?zeros of the?polynomial extremal in the?-metric with respect to a?measure with finitely many points of growth is studied under the?assumption that
On the Asymptotics of the Ratio of Orthogonal Polynomials. Ii
Let be a positive measure on the circumference and let almost everywhere on . Let be the orthogonal polynomials corresponding to , and let be their parameters. Then .Bibliography: 5 titles.
EQUILIBRIUM MEASURE AND THE DISTRIBUTION OF ZEROS OF EXTREMAL POLYNOMIALS
The authors prove a theorem which characterizes the limit distribution of the zeros of polynomials , , defined by one (for each ) extremal relation with a variable (depending on ) weight
ON ASYMPTOTIC PROPERTIES OF POLYNOMIALS ORTHOGONAL ON THE REAL AXIS
This paper contains a number of results on the logarithmic asymptotics and the asymptotic distribution of zeros of polynomials that are orthonormal on the real axis or semiaxis with respect to weight
Orthogonal Polynomials and $S$-curves
This paper is devoted to a study of $S$-curves, that is systems of curves in the complex plane whose equilibrium potential in a harmonic external field satisfies a special symmetry property
Families of equilibrium measures in an external field on the real axis
The equilibrium measure in an external field on the real axis and quantities related to this concept are studied in their dependence on the mass of the equilibrium measure.
Hermite-Pade approximants for systems of Markov-type functions
The Hermite-Pade approximants are studied for systems of Markov functions (introduced in this paper) with structure described by a graph. Results of an asymptotic nature are stated in terms of
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