Abstract harmonic analysis of continuous wavelet transforms
Author(s)
Bibliographic Information
Abstract harmonic analysis of continuous wavelet transforms
（Lecture notes in mathematics, 1863）
Springer, c2005
Available at / 66 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
L/N||LNM||186305004267
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INTERNATIONAL CHRISTIAN UNIVERSITY LIBRARY図
V.1863410.8/L507/v.186306269272,
410.8/L507/v.186306269272 -
Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
DC22:515.243/F9552080023577
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Note
Includes bibliographical references (p. [185]-190) and index
Description and Table of Contents
Description
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 volume can also be read as a problem-driven introduction to the Plancherel formula.
Table of Contents
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.
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