Fȭhr, Hartmut. <br/><br/>
Abstract Harmonic Analysis of Continuous Wavelet Transforms  [electronic resource] / 
by Hartmut Fȭhr. 
 - X, 193 p.  online resource. 
 - Lecture Notes in Mathematics,  1863  1617-9692 ; .
 - Lecture Notes in Mathematics,  1863 .
<br/><br/>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. 
<br/><br/>ZDB-2-SMA ZDB-2-LNM 
<br/><br/> 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. 
<br/><br/><label>ISBN: </label>9783540315520 
<br/><br/><label>Standard No.: </label>10.1007/b104912  doi 
<br/><br/><label>Subjects--Topical Terms: </label><br/>Mathematics.<br/>Harmonic analysis.<br/>Fourier analysis.<br/>Mathematics.<br/>Abstract Harmonic Analysis.<br/>Fourier Analysis.
<br/><br/><label>LC Class. No.: </label>QA403-403.3 
<br/><br/><label>Dewey Class. No.: </label>515.785