Introduction to Radon Transforms

With Elements of Fractional Calculus and Harmonic Analysis
2. Revised Auflage 2026
ISBN: 978-1-009-78644-7
Verlag: Cambridge University Press

Buch, Englisch, 735 Seiten

Reihe: Encyclopedia of Mathematics and its Applications

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. Fields of application include modern analysis, integral and convex geometry, and medical imaging. The text contains many examples and detailed proofs, making it accessible to graduate students and advanced undergraduates. The new edition includes four new chapters covering topics including integral geometry on lower-dimensional surfaces, tangency problems in integral geometry, and applications to convex geometry.

Autoren/Hrsg.

Rubin, Boris

Inhaltsverzeichnis

Preface to the second edition; Preface; Notation and conventions; 1. Preliminaries; 2. Fractional integration: functions of one variable; 3. Riesz potentials; 4. The Radon Transform on Rn; 5. Some operators connected with the Radon Transform; 6. Integral geometry on the unit sphere; 7. Integral geometry in the real hyperbolic space; 8. Spherical mean transforms; 9. Integral geometry on lower dimensional surfaces; 10. Tangency problems in integral geometry; 11. Some applications to convex geometry; A. Harmonic analysis on the unit sphere in Rn; Bibliography; Index.

Über Autor(innen)

Rubin, Boris
Boris Rubin is Professor of Mathematics at Louisiana State University in Baton Rouge, Louisiana. His interests include applications of fractional integrals and harmonic analysis to integral geometry. He is an author of many articles on this subject and a book Fractional Integrals, Potentials, and Radon Transforms (2024). He is Honorary Editor of the journal Fractional Calculus and Applied Analysis.