A Survey of Projective Multiresolution Analyses and a Projective Multiresolution Analysis Corresponding to the Quincunx Lattice

  • Judith A. Packer
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)


We give a survey of the concept of projective multiresolution analyses as introduced by M. Rieffel and studied further by M. Rieffel and the author. We give examples of projective multiresolution analyses corresponding to the nondiagonal 2 × 2 integer dilation matrix \(\left( {\begin{array}{*{20}c} 0&1\\ 2&0\\ \end{array}} \right)\) that has determinant -2, and also to the nondiagonal 2 × 2 matrix \(\left( {\begin{array}{*{20}c} 1&1\\ {-1}&1\\ \end{array}} \right)\) having determinant 2 related to the quincunx lattice. The method of construction follows that given by Rieffel and the author in their earlier work but also poses new problems. In both examples given here, the one-dimensional initial C(T2)-modules are not free, but the in the quincunx case, the one-dimensional wavelet module is free, whereas in the case corresponding to the dilation matrix whose determinant is negative, the one-dimensional wavelet module is not free either.


Scaling Function Projective Module Multiresolution Analysis Tight Frame Hilbert Module 
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Copyright information

© Birkhäuser Boston 2008

Authors and Affiliations

  • Judith A. Packer
    • 1
  1. 1.Department of MathematicsUniversity of Colorado at BoulderBoulder

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