Simple Wavelet Sets for Scalar Dilations in ℝ2

  • Kathy D. Merrill
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)


Wavelet sets for dilation by any scalar d > 1 in L2(ℝ2) are constructed that are finite unions of convex polygons. Such simple wavelet sets for dilation by 2 were widely conjectured to be impossible. The examples are built using the generalized scaling set technique of Baggett et al. [3]. Generalizations to other expansive dilations in L2(ℝ2) are discussed.


Multiresolution Analysis Tight Frame Construction Technique Consistency Equation Scalar Dilation 


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Copyright information

© Birkhäuser Boston 2008

Authors and Affiliations

  • Kathy D. Merrill
    • 1
  1. 1.Department of MathematicsColorado CollegeColorado Springs

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