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Overview
Written by a leading scholar in mathematics, this monograph discusses the Radon transform, a field that has wide ranging applications to X-ray technology, partial differential equations, nuclear magnetic resonance scanning and tomography. In this book, Ehrenpreis focuses on recent research and highlights the strong relationship between high-level pure mathematics and applications of the Radon transform to areas such as medical imaging.
Synopsis
Ehrenpreis (mathematics, Temple U.) examines the Radon transform, which he describes as consisting of "spread functions," or those "constant in certain directions or, more generally, which satisfy partial differential or more complicated equations." Parameters for these equations are data for Cauchy- or Dirichlet-like problems. He begins by describing the basics, then examines such topics as nonparametric Radon transforms in terms of Fourier transforms, tensor products and their topology, support conditions, harmonic functions, nonlinear Radon and Fourier transforms, and Radon transform in groups. He describes extending solutions of differential equations and closes by examining periods of Eisenstein and Poincare series. An appendix examining problems of integral geometry arising in tomography is included. Annotation ©2004 Book News, Inc., Portland, OR