Skip to main content
SpringerLink
Log in

Extensions of Szegö's theory of orthogonal polynomials

  • II. Conferenciers Ou Contributeurs
  • Conference paper
  • First Online:
Polynômes Orthogonaux et Applications

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1171))

This paper is dedicated to my friends Attila Máté and Vili Totik on the occasion of their combined seventieth birthday

This material is based upon research supported by the National Science Foundation under Grant No. MCS-83-00882.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. S. N. Bernstein, On orthogonal polynomials on a finite interval (in French), J. Mathématiques 9(1930), 127–177 and 10(1931), 219–286.

    Google Scholar 

  2. G. Freud, Orthogonal Polynomials, Pergamon Press, New York, 1971.

    MATH  Google Scholar 

  3. L. Ya. Geronimus, Orthogonal Polynomials, Consultants Bureau, New York, 1961.

    MATH  Google Scholar 

  4. U. Grenander and G. Szegö, Toeplitz Forms and Their Applications, University of California Press, Berkeley and Los Angeles, 1958.

    MATH  Google Scholar 

  5. A. N. Kolmogorov, Stationary sequences in Hilbert spaces (in Russian), Bull. Moscow State University 2:6(1941), 1–40.

    MathSciNet  Google Scholar 

  6. M. G. Krein, Generalization of investigations of G. Szegö, V. I. Smirnov and A. N. Kolmogorov (in Russian), Doklady Akad. Nauk SSSR 46(1945), 91–94.

    MathSciNet  MATH  Google Scholar 

  7. A. Máté and P. Nevai, Remarks on E. A. Rahmanov's paper "On the asymptotics of the ratio of orthogonal polynomials", J. Approximation Th. 36(1982), 64–72.

    Article  MATH  Google Scholar 

  8. A. Máté, P. Nevai and V. Totik, What is beyond Szegö's theory of orthogonal polynomials, in "Rational Approximation and Interpolation", ed. P. R. Graves-Morris et al., Springer-Verlag, LN 1105, 1984, 502–510.

    Google Scholar 

  9. A. Máté, P. Nevai and V. Totik, Asymptotics for the ratio of leading coefficients of orthonormal polynomials on the unit circle, Constructive Approximation 1(1985), 63–69.

    Article  MathSciNet  MATH  Google Scholar 

  10. A. Máté, P. Nevai and V. Totik, Strong and weak convergence of orthogonal polynomials, manuscript.

    Google Scholar 

  11. A. Máté, P. Nevai and V. Totik, Necessary conditions for weighted mean convergence of orthogonal polynomials, manuscript.

    Google Scholar 

  12. A. Máté, P. Nevai and V. Totik, Oscillatory behavior of orthogonal polynomials, manuscript.

    Google Scholar 

  13. A. Máté, P. Nevai and V. Totik, Mean Cesaro summability of orthogonal polynomials, manuscript.

    Google Scholar 

  14. A. Máté, P. Nevai and V. Totik, Extensions of Szegö's theory of orthogonal polynomials, II, manuscript.

    Google Scholar 

  15. A. Máté, P. Nevai and V. Totik, Extensions of Szegö's theory of orthogonal polynomials, III, manuscript.

    Google Scholar 

  16. P. Nevai, Orthogonal Polynomials, Memoirs of the Amer. Math. Soc., vol. 213, Providence, Rhode Island, 1979.

    Google Scholar 

  17. P. Nevai, Orthogonal polynomials defined by a recurrence relation, Trans. Amer. Math. Soc. 250(1979), 369–384.

    Article  MathSciNet  MATH  Google Scholar 

  18. F. Pollaczek, On a Generalization of Jacobi Polynomials (in French), Mémorial des Sciences Mathématiques, vol. 131, Paris, 1956.

    Google Scholar 

  19. E. A. Rahmanov, On the asymptotics of the ratio of orthogonal polynomials, Math. USSR Sbornik 32(1977), 199–213.

    Article  MathSciNet  Google Scholar 

  20. E. A. Rahmanov, On the asymptotics of the ratio of orthogonal polynomials, II, Math. USSR Sbornik 46(1983), 105–117.

    Article  Google Scholar 

  21. G. Szegö, Orthogonal Polynomials, 4th ed., Amer. Math. Soc. Colloquium Publ. vol. 23, Providence, Rhode Island, 1975.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, The Ohio State University, 43210, Columbus, OH

    Paul Nevai

Authors
  1. Paul Nevai
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Claude Brezinski André Draux Alphonse P. Magnus Pascal Maroni André Ronveaux

Rights and permissions

Reprints and permissions

Copyright information

© 1985 Springer-Verlag

About this paper

Cite this paper

Nevai, P. (1985). Extensions of Szegö's theory of orthogonal polynomials. In: Brezinski, C., Draux, A., Magnus, A.P., Maroni, P., Ronveaux, A. (eds) Polynômes Orthogonaux et Applications. Lecture Notes in Mathematics, vol 1171. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0076548

Download citation

  • DOI: https://doi.org/10.1007/BFb0076548

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16059-5

  • Online ISBN: 978-3-540-39743-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation