Advertisement

Abstract

In this paper complex contour integral representations (with non-compact paths) of cardinal exponential and logarithmic spline functions are established via the inverse bilateral Laplace transform and the inverse unilateral Mellin transform, respectively. An application of Cauchy’s residue theorem allows to determine the asymptotic behaviour of these splines as their degrees tend to infinity.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literatur

  1. 1.
    Newman, D.J., Schoenberg, I.J.: Splines and the logarithmic function. Pacific J. Math. 61, 241–258 (1975)CrossRefGoogle Scholar
  2. 2.
    Schempp, W.: A note on the Newman-Schoenberg phenomenon. Math. Z. 167, 1–6 (1979)CrossRefGoogle Scholar
  3. 3.
    Schempp, W.: Cardinal exponential splines and Laplace transform. J. Approx. Theory 31, 261–271 (1981)CrossRefGoogle Scholar
  4. 4.
    Schempp, W.: A contour integral representation of Euler-Frobenius polynomials. J. Approx. Theory 31, 272–278 (1981)CrossRefGoogle Scholar
  5. 5.
    Schempp, W.: Cardinal logarithmic splines and Mellin transform. J. Approx. Theory 31, 279–287 (1981)CrossRefGoogle Scholar
  6. 6.
    Schempp, W.: On cardinal exponential splines of higher order. J. Approx. Theory 31, 288–297 (1981)CrossRefGoogle Scholar
  7. 7.
    Schempp, W.: Complex contour integral representation of cardinal spline functions. Contemporary Mathematics, Vol. 7. Providence, R.I.: Amer. Math. Soc. 1982Google Scholar
  8. 8.
    Schoenberg, I.J.: Cardinal spline interpolation. Regional Conference Series in Applied Mathematics, Vol. 12. Philadelphia, Pennsylvania: SIAM 1973CrossRefGoogle Scholar

Copyright information

© Springer Basel AG 1983

Authors and Affiliations

  • Walter Schempp
    • 1
  1. 1.Lehrstuhl für Mathematik IUniversität SiegenSiegenDeutschland

Personalised recommendations