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Abstract Harmonic Analysis of Continuous Wavelet Transforms (Lecture Notes in Mathematics)

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Abstract Harmonic Analysis of Continuous Wavelet Transforms (Lecture Notes in Mathematics) by Hartmut Führ
English | Apr 6, 2005 | ISBN: 3540242597 | 193 Pages | PDF | 1 MB
This volume contains a systematic discussion of wavelet-type inversion formulae based on group representations, and their close connection to the Plancherel formula for locally compact groups.

Abstract Harmonic Analysis of Continuous Wavelet Transforms (Lecture Notes in Mathematics)
The connection is demonstrated by the discussion of a toy example, and then employed for two purposes: Mathematically, it serves as a powerful tool, yielding existence results and criteria for inversion formulae which generalize many of the known results. Moreover, the connection provides the starting point for a – reasonably self-contained – exposition of Plancherel theory. Therefore, the volume can also be read as a problem-driven introduction to the Plancherel formula.
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