Multivariate Anisotropic Interpolation on the Torus

  • Ronny Bergmann
  • Jürgen Prestin
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 83)


We investigate the error of periodic interpolation, when sampling a function on an arbitrary pattern on the torus. We generalize the periodic Strang-Fix conditions to an anisotropic setting and provide an upper bound for the error of interpolation. These conditions and the investigation of the error especially take different levels of smoothness along certain directions into account.


Anisotropic periodic interpolation Shift invariant spaces Lattices Interpolation error bounds 



We thank both the anonymous reviewers for their valuable remarks which improved the presentation of this paper.


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Department of MathematicsUniversity KaiserslauternKaiserslauternGermany
  2. 2.Institute of MathematicsUniversity of LübeckLübeckGermany

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