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Mat. Sb. (N.S.), 1982, Volume 119(161), Number 2(10), Pages 163–203 (Mi msb2843)  

This article is cited in 76 scientific papers (total in 76 papers)

On asymptotic properties of polynomials orthogonal on the real axis

E. A. Rakhmanov


Abstract: 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 $\mathbf R=(-\infty,+\infty)$ or semiaxis $\mathbf R_+=[0,+\infty)$ with respect to weight functions of the type $\exp(-|x|^{\lambda})$.
Bibliography: 10 titles.

Full text: PDF file (1716 kB)
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English version:
Mathematics of the USSR-Sbornik, 1984, 47:1, 155–193

Bibliographic databases:

UDC: 517.5
MSC: Primary 41A60, 42C05; Secondary 26C10, 30C15, 30E15, 31A99, 33A30, 33A65
Received: 15.11.1981

Citation: E. A. Rakhmanov, “On asymptotic properties of polynomials orthogonal on the real axis”, Mat. Sb. (N.S.), 119(161):2(10) (1982), 163–203; Math. USSR-Sb., 47:1 (1984), 155–193

Citation in format AMSBIB
\Bibitem{Rak82}
\by E.~A.~Rakhmanov
\paper On asymptotic properties of polynomials orthogonal on the real axis
\jour Mat. Sb. (N.S.)
\yr 1982
\vol 119(161)
\issue 2(10)
\pages 163--203
\mathnet{http://mi.mathnet.ru/msb2843}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=675192}
\zmath{https://zbmath.org/?q=an:0522.42018|0509.42029}
\transl
\jour Math. USSR-Sb.
\yr 1984
\vol 47
\issue 1
\pages 155--193
\crossref{https://doi.org/10.1070/SM1984v047n01ABEH002636}


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    2. Paul Nevai, “Exact Bounds for orthogonal polynomials associated with exponential weights”, Journal of Approximation Theory, 44:1 (1985), 82  crossref
    3. D.S Lubinsky, “Estimates of Freud-Christoffel functions for some weights with the whole real line as support”, Journal of Approximation Theory, 44:4 (1985), 343  crossref
    4. Attila MáTé, Paul Nevai, Vilmos Totik, “Asymptotics for the Greatest Zeros of Orthogonal Polynomials”, SIAM J Math Anal, 17:3 (1986), 745  crossref  mathscinet  zmath  isi
    5. Alphonse P Magnus, “On Freud's equations for exponential weights”, Journal of Approximation Theory, 46:1 (1986), 65  crossref
    6. Paul Nevai, “Géza Freud, orthogonal polynomials and Christoffel functions. A case study”, Journal of Approximation Theory, 48:1 (1986), 3  crossref
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    12. Mhaskar H., “Some Discrepancy Theorems”, Lect. Notes Math., 1287 (1987), 117–131  crossref  mathscinet  zmath  isi
    13. Vanassche W., “Asymptotics for Orthogonal Polynomials”, Lect. Notes Math., 1265 (1987), 1+  crossref  mathscinet  isi
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  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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