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Abstract Harmonic Analysis of Continuous Wavelet Transforms

Abstract Harmonic Analysis of Continuous Wavelet Transforms

Paperback

Series: Lecture Notes in Mathematics, Book 1863

General Mathematics

ISBN10: 3540242597
ISBN13: 9783540242598
Publisher: Springer
Published: Feb 11 2005
Pages: 193
Weight: 0.70
Height: 0.50 Width: 6.10 Depth: 9.10
Language: English

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. 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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General Mathematics