Abstract Harmonic Analysis of Continuous Wavelet Transforms
Führ, Hartmut.
Abstract Harmonic Analysis of Continuous Wavelet Transforms [electronic resource] / by Hartmut Führ. - X, 193 p. online resource. - Lecture Notes in Mathematics, 1863 0075-8434 ; . - Lecture Notes in Mathematics, 1863 .
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.
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.
9783540315520
10.1007/b104912 doi
Harmonic analysis.
Fourier analysis.
Abstract Harmonic Analysis.
Fourier Analysis.
QA403-403.3
515.785
Abstract Harmonic Analysis of Continuous Wavelet Transforms [electronic resource] / by Hartmut Führ. - X, 193 p. online resource. - Lecture Notes in Mathematics, 1863 0075-8434 ; . - Lecture Notes in Mathematics, 1863 .
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.
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.
9783540315520
10.1007/b104912 doi
Harmonic analysis.
Fourier analysis.
Abstract Harmonic Analysis.
Fourier Analysis.
QA403-403.3
515.785