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Mat. Sb. (N.S.), 1984, Volume 125(167), Number 2(10), Pages 231–258 (Mi msb2080)  

This article is cited in 73 scientific papers (total in 74 papers)

Asymptotic properties of polynomials orthogonal on a system of contours, and periodic motions of Toda lattices

A. I. Aptekarev


Abstract: An expression in the form of a Riemann theta-function is obtained for the asymptotic behavior of polynomials orthogonal on a system of contours. Properties of a limit-periodic discrete Sturm–Liouville operator and the dynamics of a periodic Toda lattice are considered as a consequence of the asymptotic formulas obtained.
Figures: 2.
Bibliography: 21 titles.

Full text: PDF file (1330 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Sbornik, 1986, 53:1, 233–260

Bibliographic databases:

UDC: 517.51+517.9+530.145
MSC: Primary 30E15, 34C25, 42C05; Secondary 14K25, 34A34, 34B25
Received: 16.06.1983

Citation: A. I. Aptekarev, “Asymptotic properties of polynomials orthogonal on a system of contours, and periodic motions of Toda lattices”, Mat. Sb. (N.S.), 125(167):2(10) (1984), 231–258; Math. USSR-Sb., 53:1 (1986), 233–260

Citation in format AMSBIB
\Bibitem{Apt84}
\by A.~I.~Aptekarev
\paper Asymptotic properties of polynomials orthogonal on a~system of contours, and periodic motions of Toda lattices
\jour Mat. Sb. (N.S.)
\yr 1984
\vol 125(167)
\issue 2(10)
\pages 231--258
\mathnet{http://mi.mathnet.ru/msb2080}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=764479}
\zmath{https://zbmath.org/?q=an:0608.42016}
\transl
\jour Math. USSR-Sb.
\yr 1986
\vol 53
\issue 1
\pages 233--260
\crossref{https://doi.org/10.1070/SM1986v053n01ABEH002918}


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    1. Nevai P., “Freud,Geza, Orthogonal Polynomials and Christoffel Functions - a Case-Study”, J. Approx. Theory, 48:1 (1986), 3–167  crossref  mathscinet  zmath  isi
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    6. John Zhang, “Relative growth of linear iterations and orthogonal polynomials on several intervals”, Linear Algebra and its Applications, 186 (1993), 97  crossref
    7. Vanassche W., “Christoffel Functions and Turan Determinants on Several Intervals”, J. Comput. Appl. Math., 48:1-2 (1993), 207–223  crossref  mathscinet  isi
    8. A. I. Aptekarev, J. S. Dehesa, R. J. Yáñez, “Spatial entropy of central potentials and strong asymptotics of orthogonal polynomials”, J Math Phys (N Y ), 35:9 (1994), 4423  crossref  zmath  adsnasa
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