Abstract Harmonic Analysis of Continuous Wavelet Transforms
- Author
- Hartmut Führ
- Publication Year
- 2005
- Publisher
- Springer
- Language
- English
- Document Type
- Book
- Faculty / Subject Heading
- Mathematics and Statistics
- Download Book Read book
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 book can also be read as a problem-driven introduction to the Plancherel formula.
Keywords: Mathematics and Statistics / Heisenberg group / Plancherel theory / Continuous wavelet transforms / Harmonic analysis / Sampling theory
