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＜電子ブック＞
Abstract Harmonic Analysis of Continuous Wavelet Transforms / by Hartmut Führ
(Lecture Notes in Mathematics. ISSN:16179692 ; 1863)

版	1st ed. 2005.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2005
本文言語	英語
大きさ	X, 193 p : online resource
著者標目	*Führ, Hartmut author SpringerLink (Online service)
件　名	LCSH:Harmonic analysis LCSH:Fourier analysis FREE:Abstract Harmonic Analysis FREE:Fourier Analysis
一般注記	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 HTTP:URL=https://doi.org/10.1007/b104912

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