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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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What parts of a measure’s support attract zeros of the corresponding orthogonal polynomials?
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by E. B. Saff and Vilmos Totik PDF
Proc. Amer. Math. Soc. 114 (1992), 185-190 Request permission

Abstract:

It is proved that each "component" of the polynomial convex hull of the support of the generating measure attracts zeros of the corresponding orthogonal polynomials. On the other hand, an example is given showing e.g. that mass points in the support need not attract zeros.
References
    G. Freud, Orthogonal polynomials, Akad. Kiadó, Budapest, 1971.
  • E. B. Saff, Orthogonal polynomials from a complex perspective, Orthogonal polynomials (Columbus, OH, 1989) NATO Adv. Sci. Inst. Ser. C: Math. Phys. Sci., vol. 294, Kluwer Acad. Publ., Dordrecht, 1990, pp. 363–393. MR 1100302, DOI 10.1007/978-94-009-0501-6_{1}7
  • Herbert Stahl and Vilmos Totik, General orthogonal polynomials, Encyclopedia of Mathematics and its Applications, vol. 43, Cambridge University Press, Cambridge, 1992. MR 1163828, DOI 10.1017/CBO9780511759420
  • Herbert Stahl and Vilmos Totik, $n$th root asymptotic behavior of orthonormal polynomials, Orthogonal polynomials (Columbus, OH, 1989) NATO Adv. Sci. Inst. Ser. C: Math. Phys. Sci., vol. 294, Kluwer Acad. Publ., Dordrecht, 1990, pp. 395–417. MR 1100303
  • Pál Turán, On some open problems of approximation theory, Mat. Lapok 25 (1974), no. 1-2, 21–75 (1977) (Hungarian). MR 442540
  • Harold Widom, Polynomials associated with measures in the complex plane, J. Math. Mech. 16 (1967), 997–1013. MR 0209448
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Additional Information
  • © Copyright 1992 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 114 (1992), 185-190
  • MSC: Primary 42C05; Secondary 30C99
  • DOI: https://doi.org/10.1090/S0002-9939-1992-1077789-X
  • MathSciNet review: 1077789