Skip to main content

A pólya algorithm for the favard solution, N-width characterizations and Whitney type theorems

  • Part VIII. Further Topics
  • Chapter
  • First Online:
  • 277 Accesses

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 479))

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   54.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   69.99
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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. C. DeBoor, “On best interpolation,” J. of Approximation Theory, to appear.

    Google Scholar 

  2. C. K. Chui, P. W. Smith, and J. D. Ward, “Favard’s solution is the limit of Wk, p-splines,” manuscript.

    Google Scholar 

  3. C. Coatmelec, “Prolongement d’une fonction en une fonction differentiable. Diverses majorations sur le prolongement,” in, Approximation with Special Emphasis on Spline Functions, I. J. Schoenberg, Ed., Academic Press, New York, 1969, pp. 29–49.

    Google Scholar 

  4. J. Favard, “Sur l’interpolation,” J. Math. Pures et Appliques, 19 (1940), 281–306.

    MathSciNet  MATH  Google Scholar 

  5. G. Glaeser, “Prolongement extremal de fonctions differentiables d’une variable,” J. Approximation Theory, 8 (1973), 249–261.

    Article  MathSciNet  MATH  Google Scholar 

  6. M. Golomb, “Hm, p-extensions by Hm, p-splines,” J. of Approximation Theory, 5 (1972), 238–275.

    Article  MathSciNet  MATH  Google Scholar 

  7. M. Golomb and J. Jerome, “Linear ordinary differential equations with boundary conditions on arbitrary point sets,” Trans. Amer. Math. Soc., 153 (1971), 235–264.

    Article  MathSciNet  MATH  Google Scholar 

  8. J. W. Jerome and L. L. Schumaker, “Characterizations of absolute continuity and essential boundedness for higher order derivatives,” J. Math. Anal. Appl., 42 (1973), 452–465.

    Article  MathSciNet  MATH  Google Scholar 

  9. A. N. Kolmogorov, “Über die beste Annäherung von Functionen einer gegebenen Funktionklasse,” Ann. Math., (2), 37 (1936), 107–111.

    Article  MathSciNet  Google Scholar 

  10. F. Riesz, “Systeme integrierbarer Funktionen,” Math. Ann., 69 (1910), 449–497.

    Article  MathSciNet  MATH  Google Scholar 

  11. I. J. Schoenberg, “Spline interpolation and the higher derivatives,” Proc. Nat. Acad. Sci. U.S.A., 51 (1964), 24–28.

    Article  MathSciNet  MATH  Google Scholar 

  12. P. W. Smith, “Wr, p(R)-Splines,” dissertation, Purdue University, Lafayette, Indiana, June, 1972.

    Google Scholar 

  13. -, “Hr, ∞(R) and Wr, ∞(R)-splines,” Trans. Amer. Math. Soc., 192 (1974), 275–284.

    MathSciNet  Google Scholar 

  14. V. M. Tihomirov, “On n-dimensional diameters of certain functional classes,” Soviet Math.-Doklady, 1 (1960), 94–97.

    MathSciNet  Google Scholar 

  15. -, “Diameters of sets in function spaces and the theory of best approximations,” Uspehi 15 No. 3 (93) (1960), 81–120.

    MathSciNet  Google Scholar 

  16. -, “Some problems of approximation theory,” Soviet Math., 6 (1965), 202–205.

    MathSciNet  Google Scholar 

  17. -, “Best methods of approximation and interpolation of differentiable functions in the space C[−1, 1],” Math. USSR-Sb., 9 (1969), 275–289.

    Article  MathSciNet  Google Scholar 

  18. H. Whitney, “Differentiable functions defined in closed sets.” Trans. Amer. Math. Soc. 36 (1934), 369–337.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1975 Springer-Verlag

About this chapter

Cite this chapter

Fisher, S.D., Jerome, J.W. (1975). A pólya algorithm for the favard solution, N-width characterizations and Whitney type theorems. In: Minimum Norm Extremals in Function Spaces. Lecture Notes in Mathematics, vol 479. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0097075

Download citation

  • DOI: https://doi.org/10.1007/BFb0097075

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07394-9

  • Online ISBN: 978-3-540-37599-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics