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Simple Wavelet Sets for Scalar Dilations in ℝ2

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

Abstract

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.

Keywords

Multiresolution Analysis Tight Frame Construction Technique Consistency Equation Scalar Dilation 
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

© Birkhäuser Boston 2008

Authors and Affiliations

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

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