Lecture Notes in Mathematics - Abstract Harmonic Analysis of Continuous Wavelet Transforms

This volume discusses a construction situated at the intersection of two different mathematical fields: Abstract harmonic analysis, understood as the theory of group representations and their decomposition into irreducibles on the one hand, and wavelet (and related) transforms on the other. In a sense the volume reexamines one of the roots of wavelet analysis: The paper [60] by Grossmann, Morlet and Paul may be considered as one of the initial sources of wavelet theory, yet it deals with a unitary representation of the affine group, citing results on discrete series representations of nonunimodular groups due to Duflo and Moore. It was also observed in [60] that the discrete series setting provided a unified approach to wavelet as well as other related transforms, such as the windowed Fourier transform.

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