Orthogonalization and isospectral approximation

  • Ola Bratteli
  • Palle Jorgensen
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)


The need for the more general wavelet families is motivated already on the grounds of symmetry in the dyadic case, as follows: recall that in order to obtain compactly supported wavelets that are continuous as well as symmetric, or antisymmetric, one has to abandon orthogonality. This was noted in Chapter 2, while in the exercises of Chapter 1, we recall that the splines serve as examples with symmetry, or antisymmetry. The theorems which exclude an axis of antisymmetry for the real-valued continuous and compactly supported dyadic wavelet functions center around [Dau92, Theorem 8.1.4 and Remark 2, p. 253].


Matrix Function Transfer Operator Tight Frame Wavelet Filter Biorthogonal Wavelet 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media New York 2002

Authors and Affiliations

  • Ola Bratteli
    • 1
  • Palle Jorgensen
    • 2
  1. 1.Department of MathematicsUniversity of IowaIowa CityUSA
  2. 2.Department of MathematicsUniversity of OsloOsloNorway

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