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.
| ISBN: | 9780521854597 |
| Publication date: | 12th November 2015 |
| Author: | Boris Rubin |
| Publisher: | Cambridge University Press |
| Format: | Hardback |
| Pagination: | 596 pages |
| Series: | Encyclopedia of Mathematics and its Applications |
| Genres: |
Functional analysis and transforms |
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.
Introduction to Radon Transforms features in the following genres: Functional analysis and transforms
Introduction to Radon Transforms is available in Hardback
Introduction to Radon Transforms was written by Boris Rubin and published by Cambridge University Press
Introduction to Radon Transforms has 596 pages
Yes it is part of Encyclopedia of Mathematics and its Applications series
£155.70