Box Splines pp 79-103 | Cite as

Cardinal interpolation & difference equations

  • Carl de Boor
  • Klaus Höllig
  • Sherman Riemenschneider
Part of the Applied Mathematical Sciences book series (AMS, volume 98)


In this chapter, we consider cardinal interpolation, i.e., the interpolation to data on the integer mesh, from a space of cardinal splines. This problem is intimately connected to the solution of a multivariate difference equation, and the qualitative properties of the interpolation, its correctness or singularity, are determined by the symbol of the difference equation.


Difference Equation Fundamental Solution Linear Independence Fundamental Function Poisson Summation Formula 
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Copyright information

© Springer Science+Business Media New York 1993

Authors and Affiliations

  • Carl de Boor
    • 1
  • Klaus Höllig
    • 2
  • Sherman Riemenschneider
    • 3
  1. 1.Center for Mathematical SciencesUniversity of Wisconsin-MadisonMadisonUSA
  2. 2.Math Institut A der UniversitätStuttgart 80Germany
  3. 3.Department of MathematicsUniversity of AlbertaEdmontonCanada

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