TY  - BOOK
AU  - 
ED  - SpringerLink (Online service)
TI  - Abstract Harmonic Analysis of Continuous Wavelet Transforms
T2  - Lecture Notes in Mathematics,
SN  - 9783540315520
AV  - QA403-403.3 
U1  - 515.785 23
PY  - 2005///
CY  - Berlin, Heidelberg
PB  - Springer Berlin Heidelberg
KW  - Mathematics
KW  - Harmonic analysis
KW  - Fourier analysis
KW  - Abstract Harmonic Analysis
KW  - Fourier Analysis
N1  - Introduction -- Wavelet Transforms and Group Representations -- The Plancherel Transform for Locally Compact Groups -- Plancherel Inversion and Wavelet Transforms -- Admissible Vectors for Group Extension -- Sampling Theorems for the Heisenberg Group -- References -- Index; ZDB-2-SMA; ZDB-2-LNM
N2  - 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
UR  - http://dx.doi.org/10.1007/b104912
ER  -