Skip to main content

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 133))

Abstract

We plan to examine collections of orthogonal polynomials satisfying second, fourth and higher order differential equations in detail. However, since they have a great deal in common, we develop that common ground here.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 69.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 89.99
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. L. C. Andrews, Special Functions for Engineers and Applied Mathematicians, Macmillan, New York, 1985.

    Google Scholar 

  2. R. P. Boas, The Stieltjes moment problem for functions of bounded variation, Bull. Amer. Math. Soc. 45 (1939), 399–404.

    Article  MathSciNet  Google Scholar 

  3. T. S. Chihara, An Introduction to Orthogonal Polynomials, Gordon and Breach, New York, 1978.

    MATH  Google Scholar 

  4. A. J. Duran, The Stieltjes moment problem for rapidly decreasing functions, Proc. Amer. Math. Soc. 107 (1989), 731–741.

    Google Scholar 

  5. H. L. Krall, Certain differential equations for Tchebycheff polynomials, Duke Math. J. 4 (1938), 705–718.

    Article  MathSciNet  Google Scholar 

  6. —, Self-adjoint differential expressions, Amer. Math. Monthly 67 (1960), 867–878.

    Article  MathSciNet  Google Scholar 

  7. K. H. Kwon, L. L. Littlejohn and B. H. Yoo, Characterizations of orthogonal polynomials satisfying certain differential equations, SIAM J. Math. Anal. 1 (1993), 10–24.

    Google Scholar 

  8. L. L. Littlejohn and D. Race, Symmetric and symmetrisable differential expressions, Proc. London Math Soc. 60 (1990), 344–364.

    Article  MathSciNet  MATH  Google Scholar 

  9. R. D. Morton and A. M. Krall, Distributional weight functions and orthogonal polynomials, SIAM J. Math. Anal. 9 (1978), 604–626.

    Article  MathSciNet  MATH  Google Scholar 

  10. E. D. Rainville, Special Functions, Macmillan, New York, 1960.

    MATH  Google Scholar 

  11. J. A. Shohat and J. D. Tamarkin, The Problem of Moments, Amer. Math. Soc., Providence, RI, 1943.

    Google Scholar 

  12. G. Szego, Orthogonal Polynomials, Amer. Math. Soc, Providence, RI, 1939.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer Basel AG

About this chapter

Cite this chapter

Krall, A.M. (2002). Orthogonal Polynomials. In: Hilbert Space, Boundary Value Problems and Orthogonal Polynomials. Operator Theory: Advances and Applications, vol 133. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8155-5_13

Download citation

  • DOI: https://doi.org/10.1007/978-3-0348-8155-5_13

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9459-3

  • Online ISBN: 978-3-0348-8155-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics