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Rational approximations, orthogonal polynomials and equilibrium distributions

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Orthogonal Polynomials and their Applications

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1329))

Abstract

A number of questions of rational approximation and orthogonal polynomials may be reduced to some general problems concerning the equilibrium distributions of a "system of charges" on a "system of conductors" in the presence of exterior fields. The corresponding concept of equilibrium for "vector-potentials" is considered in the paper of A.A. Goncar and E.A. Rakhmanov [9]. The most simple case of a "single charge" was discused in their paper [8]. Here we consider several problems of approximation theory mainly connected with the equilibrium distributions for a single potential. We note that we do not pretend to give a complete review of all the contributions obtained in this direction, we limit ourselves to those results due to A.A.Gončar, G.López and E.A.Rakhmanov.

We begin with the following simple but important example which contains almost all the essential features.

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Author information

Authors and Affiliations

  1. Math. Dept., Hav. Univ., Havana

    G. López

  2. Steklov Math. Inst., Moscow

    E. A. Rakhmanov

Authors
  1. G. López
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  2. E. A. Rakhmanov
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Editor information

Manuel Alfaro Jesús S. Dehesa Francisco J. Marcellan José L. Rubio de Francia Jaime Vinuesa

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© 1988 Springer-Verlag

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López, G., Rakhmanov, E.A. (1988). Rational approximations, orthogonal polynomials and equilibrium distributions. In: Alfaro, M., Dehesa, J.S., Marcellan, F.J., Rubio de Francia, J.L., Vinuesa, J. (eds) Orthogonal Polynomials and their Applications. Lecture Notes in Mathematics, vol 1329. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083356

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  • DOI: https://doi.org/10.1007/BFb0083356

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  • Print ISBN: 978-3-540-19489-7

  • Online ISBN: 978-3-540-39295-8

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