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Abstract

If k is a positive integer an n-variate k-harmonic cardinal spline is a tempered distribution f on R n such that ∆ k f is a measure supported on the integer lattice Z n in R n . Symbolically
$${{\Delta }^{k}}f\left( x \right)=\sum\limits_{\text{j}\in {{\text{Z}}^{n}}}{{{a}_{j}}}\delta \left( x-j \right)$$
(1)
where ∆ is the n variate Laplacian, ∆k = ∆∆k−1 for k > 1, and δ(x) is the unit Dirac measure supported at the origin. A polyharmonic spline is one which is k-harmonic for some k.

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Copyright information

© Birkhäuser Verlag Basel 1989

Authors and Affiliations

  • W. R. Madych
    • 1
  1. 1.Department of MathematicsUniversity of ConnecticutStorrsUSA

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