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On the Nonexistence of Certain Divergence-free Multiwavelets

  • J. D. Lakey
  • M. C. Pereyra
Chapter
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Abstract

We show that there are no biorthogonal pairs of divergence-free multiwavelet families on Rnhaving any regularity, such that both biorthogonal families have compactly supported, divergence-free generators. This main result generalizes Lemarié’s bivariate result. In particular, our method is based on vector-valued multiresolution analyses.

Keywords

Compact Support Trigonometric Polynomial Multiresolution Analysis Riesz Basis Dyadic Cube 
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References

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    Lakey, J., Massopust, P., and Pereyra, M.C., Divergence-free multiwavelets, in Proc. Approximation Theory IX. 2:161–168 (1998), C. K. Chui and L. L. Schumaker (eds).MathSciNetGoogle Scholar
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Copyright information

© Springer Science+Business Media New York 2003

Authors and Affiliations

  • J. D. Lakey
  • M. C. Pereyra

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