Integral Geometry and Radon Transforms

• Main Author: Helgason, Sigurdur (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York, 2011.
• Subjects: Mathematics.; Topological groups.; Lie groups.; Global analysis (Mathematics).; Manifolds (Mathematics).; Integral transforms.; Operational calculus.; Differential geometry.; Differential Geometry.; Integral Transforms, Operational Calculus.; Global Analysis and Analysis on Manifolds.; Topological Groups, Lie Groups.

In this text, integral geometry deals with Radon’s problem of representing a function on a manifold in terms of its integrals over certain submanifolds—hence the term the Radon transform. Examples and far-reaching generalizations lead to fundamental problems such as: (i) injectivity, (ii) inversion...