The Radon Transform (Progress in Mathematics) - Sigurdur Helgason (1980)
ISBN 3764330066
Subject Radon transforms
Publisher Birkhauser
Publication Date June 1980
Format Hardcover (230 mm)
Language eng

The Radon transform is an important topic in integral geometry which deals with the problem of expressing a function on a manifold in terms of its integrals over certain submanifolds. Solutions to such problems have a wide range of applications, namely to partial differential equations, group representations, X-ray technology, nuclear magnetic resonance scanning, and tomography. This second edition, significantly expanded and updated, presents new material taking into account some of the progress made in the field since 1980.

The first chapter introduces the Radon transform and presents new material on the d-plane transform and applications to the wave equation. Chapter 2 places the Radon transform in a general framework of integral geometry known as a double fibration of a homogeneous space. Several significant examples are developed in detail. Two subsequent chapters treat some specific examples of generalized Radon transforms, for examples, antipodal manifold in compact 2-points homogeneous spaces, and orbital integrals in isotropic Lorentzian manifolds. A final chapter deals with Fourier transforms and distributions, developing all the tools needed in the work.

Aimed at beginning graduate students, this monograph will be useful in the classroom or as a resource for self-study. Readers will find here an accessible introduction to Radon transform theory, an elegant topic in integral geometry.

Personal Details
Collection Status In Collection
Index 1420
Read It Yes
Links Amazon US
Barnes & Noble
Product Details
LoC Classification QA649 .H44 1983
Dewey 516.3/6
Cover Price $38.50
No. of Pages 192
Includes index.