Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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



Orthogonal polynomials with ratio asymptotics

Author: Vilmos Totik
Journal: Proc. Amer. Math. Soc. 114 (1992), 491-495
MSC: Primary 42C05
MathSciNet review: 1065095
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A general construction is given for measures for which the corresponding orthogonal polynomials have ratio asymptotics.

References [Enhancements On Off] (What's this?)

  • [1] F. Delyon, B. Simon, and B. Souillard, From power pure point to continuous spectrum in disordered systems, Ann. Inst. H. Poincaré Phys. Théor. 42 (1985), 283-309. MR 797277 (87d:35098)
  • [2] G. Freud, Orthogonal polynomials, Akadémia Kiadó/Pergamon Press, Budapest, 1971.
  • [3] D. S. Lubinsky, Jump distributions in $ [-1,1]$ whose orthogonal polynomials have leading coefficients with a given asymptotic behavior, Proc. Amer. Math. Soc. 104 (1988), 516-524. MR 962822 (90c:42031)
  • [4] -, Singularly continuous measures in Nevai's class $ M$, Proc. Amer. Math. Soc. 111 (1991), 413-420. MR 1039259 (91f:42026)
  • [5] AI. Magnus and W. Van Assche, Sieved orthogonal polynomials and discrete measures with jumps dense in an interval, Proc. Amer. Math. Soc. 106 (1989), 163-173. MR 953001 (89i:42036)
  • [6] P. Nevai, Orthogonal polynomials, Mem. Amer. Math. Soc., no. 213, Amer. Math. Soc., Providence, RI, 1979. MR 519926 (80k:42025)
  • [7] E. A. Rahmanov, On the asymptotics of the ratio of orthonormal polynomials, Math. USSR Sb. 32 (1977), 199-213.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 42C05

Retrieve articles in all journals with MSC: 42C05

Additional Information

Keywords: Orthogonal polynomials, ratio asymptotics, class $ M$, singular measure
Article copyright: © Copyright 1992 American Mathematical Society

American Mathematical Society