Skip to main content
Log in

On monosplines with odd multiplicity of least norm

  • Published:
Journal d’Analyse Mathématique Aims and scope

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. R. B. Barrar and H. L. Loeb,On extended varisolvent families, J. Analyse Math.26 (1973), 243–254.

    MATH  MathSciNet  Google Scholar 

  2. R. B. Barrar and H. L. Loeb,Optimal integration formulas for analytic functions, Bull. Amer. Math. Soc.79 (1973), 1296–1298.

    MATH  MathSciNet  Google Scholar 

  3. R. B. Barrar and H. L. Loeb,Spline functions with free knots as the limit of varisolvent families, J. Approximation Theory12 (1974), 70–77.

    Article  MATH  MathSciNet  Google Scholar 

  4. R. B. Barrar and H. L. Loeb,Multiple zeros and applications to optimal linear functions, Numer. Math.25 (1976), 251–262.

    Article  MATH  MathSciNet  Google Scholar 

  5. R. B. Barrar and H. L. Loeb,On a nonlinear characterization problem for monosplines, J. Approximation Theory18 (1976), 220–240.

    Article  MATH  MathSciNet  Google Scholar 

  6. R. B. Barrar and H. L. Loeb,On the convergence of smooth monosplines to polynomial monosplines, to appear in Proc. Symp. on Approximation Theory, Austin, Texas, 1976.

  7. R. B. Barrar, H. L. Loeb and H. Werner,On the existence of optimal integration formulas for analytic functions, Numer. Math.23 (1974), 105–117.

    Article  MATH  MathSciNet  Google Scholar 

  8. D. Braess,Chebyshev approximation by spline functions with free knots, Numer. Math.17 (1971), 357–366.

    Article  MATH  MathSciNet  Google Scholar 

  9. D. Braess,Chebyshev approximation by γ-polynomials, J. Approximation Theory9 (1973), 20–43.

    Article  MATH  MathSciNet  Google Scholar 

  10. A. S. Cavaretta, Jr.,Oscillatory and zero properties for perfect splines and monosplines, J. Analyse Math.28 (1975), 41–59.

    MATH  Google Scholar 

  11. C. Fitzgerald and L. L. Schumaker,A differential equation approach to interpolation of extremal points, J. Analyse Math.22 (1969), 117–134.

    MATH  MathSciNet  Google Scholar 

  12. E. Isaacson and H. B. Keller,Analysis of Numerical Methods, John Wiley and Sons, Inc., New York, 1966.

    MATH  Google Scholar 

  13. R. S. Johnson,On monosplines of least deviation, Trans. Amer. Math. Soc.96 (1960), 458–477.

    Article  MathSciNet  Google Scholar 

  14. S. Karlin,Total Positivity, Stanford University Press, Stanford, 1968.

    MATH  Google Scholar 

  15. S. Karlin,On a class of best nonlinear approximation problems and extended monosplines, inStudies in Spline Functions and Approximation Theory, S. Karlin, C. Micchelli, A. Pinkus and I. J. Schoenberg (eds.), Academic Press, New York, 1976, pp. 19–59.

    Google Scholar 

  16. S. Karlin,A global improvement theorem for polynomial monosplines, inStudies in Spline Functions and Approximation Theory, S. Karlin, C. Micchelli, A. Pinkus and I. J. Schoenberg (eds.), Academic Press, New York, 1976, pp. 67–74.

    Google Scholar 

  17. S. Karlin and A. Pinkus,Gaussian quandrature formulae with multiple nodes, inStudies in Spline Functions and Approximation Theory, S. Karlin, C. Micchelli, A. Pinkus and I. J. Schoenberg (eds.), Academic Press, New York, 1976, pp. 113–137.

    Google Scholar 

  18. S. Karlin and L. L. Schumaker,The fundamental theorem of algebra for Tchebysheffian monosplines, J. Analyse Math.20 (1967), 233–270.

    Article  MATH  MathSciNet  Google Scholar 

  19. G. Meinardus,Approximation of Functions: Theory and Numerical Methods, Springer-Verlag, New York, 1967.

    MATH  Google Scholar 

  20. C. Micchelli,The fundamental theorem of algebra for mosplines with multiplicities, inLinear Operators and Approximation, P. L. Butzer et al. (eds.), Birkhauser Verlag, Basel, 1972, pp. 419–430.

    Google Scholar 

  21. J. R. Rice,The Approximation of Functions, Vol. 2, Addison-Wesley Publishing Company, Reading, Massachusetts, 1969.

    MATH  Google Scholar 

  22. I. J. Schoenberg and Z. Ziegler,On cardinal monosplines of least L -norm on the real axis, J. Analyse Math.23 (1970), 409–436.

    MATH  MathSciNet  Google Scholar 

  23. L. L. Schumaker,Uniform approximation by Chebyshev spline functions, II, Free knots, SIAM J. Numer. Anal.5 (1968), 647–656.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

We thank the referces for their excellent suggestions which greatly improved the paper.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Barrar, R.B., Loeb, H.L. On monosplines with odd multiplicity of least norm. J. Anal. Math. 33, 12–38 (1978). https://doi.org/10.1007/BF02790167

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02790167

Keywords

Navigation