The Radon transform represents a function on a manifold by its integrals over certain submanifolds. Integral transformations of this kind have a wide range of applications in modern analysis, integral and convex geometry, medical imaging, and many other areas. Reconstruction of functions from their Radon transforms requires tools from harmonic analysis and fractional differentiation. This comprehensive introduction contains a thorough exploration of Radon transforms and related operators when the basic manifolds are the real Euclidean space, the unit sphere, and the real hyperbolic space. Radon-like transforms are discussed not only on smooth functions but also in the general context of Lebesgue spaces. Applications, open problems, and recent results are also included. The book will be useful for researchers in integral geometry, harmonic analysis, and related branches of mathematics, including applications. The text contains many examples and detailed proofs, making it accessible to graduate students and advanced undergraduates.

A comprehensive introduction to basic operators of integral geometry and the relevant harmonic analysis for students and researchers.

About the Author
Boris Rubin is Professor of Mathematics at Louisiana State University. He is the author of the book Fractional Integrals and Potentials and has written more than one hundred research papers in the areas of fractional calculus, integral geometry, and related harmonic analysis.


Book Information
ISBN 9780521854597
Author Boris Rubin
Format Hardback
Page Count 596
Imprint Cambridge University Press
Publisher Cambridge University Press
Weight(grams) 1070g
Dimensions(mm) 240mm * 163mm * 41mm