Skip to main content
SpringerLink
Log in

Notes on spline functions III: On the convergence of the interpolating cardinal splines as their degree tends to infinity

  • Published:
Israel Journal of Mathematics Aims and scope Submit manuscript

Abstract

It is shown that for entire functionsf(x) defined by a Fourier-Stieltjes integral (9) the cardinal splineS m (x) of the odd degree 2m−1, which interpolatesf(x) at all integers, converges tof(x) asm tends to infinity. Properties of the exponential Euler spline are used in the proof.

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

Similar content being viewed by others

References

  1. M.v. Golitschek,On the convergence of interpolating periodic spline functions of high degree, Numer. Math.19 (1972), 146–154.

    Article  MATH  MathSciNet  Google Scholar 

  2. M. Golomb,Approximation by periodic spline interpolants on uniform meshes, J. Approximation Theory,1 (1968), 26–65.

    Article  MATH  MathSciNet  Google Scholar 

  3. W. Quade and L. Collatz,Zur Interpolationstheorie der reellen periodischen Funktionen, Sitzunsgber. Preussischen Akad. Wiss., Phys.-Math. K1 (1938), 383–429.

    Google Scholar 

  4. I. J. Schoenberg,Notes on spline functions. I. The limits of the interpolating periodic spline functions as their degree tends to infinity, MRC T. S. R. #1219, April 1972 (to appear in the Indag. Math.).

  5. I. J. Schoenberg,Cardinal interpolation and spline functions VII. The behavior of cardinal spline interpolants as their degree tends to infinity, MRC T. S. R. #1184, December 1971 (to appear in J. Analyse Math.).

  6. I. J. Schoenberg,Cardinal spline interpolation, Regional Conference Series in Applied Mathematics, No. 12, 125 pages, S. I. A. M., Philadelphia, Pa., 1973.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematics Research Center, University of Wisconsin, Madison, Wisconsin, USA

    I. J. Schoenberg

Authors
  1. I. J. Schoenberg
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Sponsored by the United States Army under Contract No. DA-31-124-ARO-D-462.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Schoenberg, I.J. Notes on spline functions III: On the convergence of the interpolating cardinal splines as their degree tends to infinity. Israel J. Math. 16, 87–93 (1973). https://doi.org/10.1007/BF02761973

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02761973

Keywords

Search

Navigation