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Characteristic Wavelet Equations and Generalizations of the Spectral Function

  • Veronika Furst
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Abstract

Two equations characterize orthonormal (and Parseval) wavelets in L2(ℝ). We trace the history and development of this characterization and present a different argument that uses a generalization of the spectral function of Bownik and Rzeszotnik. By further generalizing this function in the setting of an abstract Hilbert space, we present a compressed proof of the abstract characteristic equation.

Keywords

Spectral Function Orthonormal Wavelet Multiplicity Function Parseval Frame Countable Collection 
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

  • Veronika Furst
    • 1
  1. 1.Department of MathematicsFort Lewis CollegeDurango

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