Skip to main content
SpringerLink
Log in

Oscillatory and zero properties for perfect splines and monosplines

  • 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

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

References

  1. E. A. Conddington and N. Levinson,Theory of Ordinary Differential Equations, McGraw-Hill, New York, 1955.

    Google Scholar 

  2. J. Favard,Sur l’interpolation, J. Math. Pures Appl.104-105 (1939-40), 281–306.

    MathSciNet  Google Scholar 

  3. G. H. FitzGerald and L. L. Schumaker,A differential equation approach to interpolation at extremal points, J. Analyse Math.22 (1969) 117–134.

    MATH  MathSciNet  Google Scholar 

  4. G. Glaeser,Prolongement extrémal de fonction différentiable, Publications de la section Mathématiques de la Faculté des Sciences de Rennes, 1967.

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

    Article  MathSciNet  Google Scholar 

  6. S. Karlin,Total Positivity, Stanford University Press, 1969.

  7. S. Karlin,The fundamental theorem of algebra for monosplines satisfying certain boundary conditions and applications to optimal quadrature formulas, inApproximations with Special Emphasis on Spline Functions, I. J. Schoenberg (ed.), Academic Press, New York, 1969.

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  9. I. J. Schoenberg and A. S. Cavaretta,Solution of Landau’s problem concerning higher derivations on the halfline, to appear in Proceedings of an International Conference on Approximation Theory,Oct. 26–30, 1970, University of Maryland.

  10. I. J. Schoenberg and Ann Whitney,On Pólya frequency functions III. The positivity of translation determinants with application to the interpolation problem by spline curves, Trans. Amer. Math. Soc, 1953.

  11. V. M. Tihomirov,Best methods of approximation and interpolation of differentiable functions in the space C[-l, 1], Mat. Sb.80 (122) (1969) no. 2 (Math. USSR Sb.9 (1969), 275–289).

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Middlebury College, Middlebury, Vermont

    Alfred S. Cavaretta

  2. California Institute of Technology, Pasadena, California

    Alfred S. Cavaretta

Authors
  1. Alfred S. Cavaretta
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This work was partially supported by the National Science Foundation.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Cavaretta, A.S. Oscillatory and zero properties for perfect splines and monosplines. J. Anal. Math. 28, 41–59 (1975). https://doi.org/10.1007/BF02786805

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02786805

Keywords

Search

Navigation