Radon Transforms, Geometry, and Wavelets

by Olafsson, Gestur; Grinberg, Eric L.; Larson, David; Jorgensen, Palle E. T.; Massopust, Peter R.

• ISBN13: 9780821843277
• ISBN10: 0821843273
• Format: Paperback
• Copyright: 2008-08-31
• Publisher: Amer Mathematical Society

Summary

This volume is based on two special sessions held at the AMS Annual Meeting in New Orleans in January 2007, and a satellite workshop held in Baton Rouge on January 4-5, 2007. It consists of invited expositions that together represent a broad spectrum of fields, stressing surprising interactions and connections between areas that are normally thought of as disparate. The main topics are geometry and integral transforms. On the one side are harmonic analysis, symmetric spaces,representation theory (the groups include continuous and discrete, finite and infinite, compact and non-compact), operator theory, PDE, and mathematical probability. Moving in the applied direction we encounter wavelets, fractals, and engineering topics such as frames and signal and image processing.The subjects covered in this book form a unified whole, and they stand at the crossroads of pure and applied mathematics. The articles cover a broad range in harmonic analysis, with the main themes related to integral geometry, the Radon transform, wavelets and frame theory. These themes can loosely be grouped together as follows:Frame Theory and ApplicationsHarmonic Analysis and Function SpacesHarmonic Analysis and Number TheoryIntegral Geometry and Radon TransformsMultiresolution Analysis, Wavelets, and Applications

Table of Contents

Composite wavelet transforms: Applications and perspectives

Complex sigma-delta quantization algorithms for finite frames

Decomposition and admissibility for the quasiregular representation for generalized oscillator groups

Fourier series on fractals: A parallel with wavelet theory

A computational complexity paradigm for tomography

Invariant differential operators on matrix motion groups and applications to the matrix radon transform

Sums and products in finite fields: An integral geometric viewpoint

Frame potential and finite abelian groups

Robustness of fusion frames under erasures of subspaces and of local frame vectors

Smooth, well-localized Parseval wavelets based on wavelet sets in $\mathbb{R}^2$

Explicit schemes in seismic migration and isotropic multiscale representations

Invariant functions on Grassmannians

Harmonic analysis related to Schrodinger operators

Discrete Helgason-Fourier transform for Sobolev and Besov functions on noncompact symmetric spaces

Helgason's support theorem and spherical radon transforms

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