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Wavelet Sets

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

Abstract

Wavelet sets are intimately related to the multiplicity function of a GMRA. In this chapter, we explore how to build wavelet sets from multiplicity functions, as well as directly from the consistency equation and from their geometric properties. We focus on simple wavelet sets, those that are a finite union of convex sets. We include wavelet sets for all expansive integer matrix dilations in \(L^2(\mathbb R^N)\), and also consider multiwavelet sets and Parseval wavelet sets.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Kathy D. Merrill
    • 1
  1. 1.Department of MathematicsThe Colorado CollegeColorado SpringsUSA

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