Boris Rubin: Introduction to Radon Transforms

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Cover: 9780521854597 | Introduction to Radon Transforms | Boris Rubin | Buch | Englisch

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Sprache: Englisch

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Beschreibung

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.

Über den Autor

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.

Zusammenfassung

This comprehensive introduction for students and researchers explores Radon transforms and related operators when the basic manifolds are the real Euclidean space, the unit sphere, and the real hyperbolic space. Applications include analysis, integral and convex geometry, and medical imaging. Open problems and recent results are also presented.

Inhaltsverzeichnis

1. Preliminaries; 2. Fractional integration: functions of one variable; 3. Riesz potentials; 4. The Radon transform on Rn; 5. Operators of integral geometry on the unit sphere; 6. Operators of integral geometry in the hyperbolic space; 7. Spherical mean Radon transforms.

Erscheinungsjahr:	2015
Fachbereich:	Geometrie
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Seiten:	596
ISBN-13:	9780521854597
ISBN-10:	0521854598
Sprache:	Englisch
Ausstattung / Beilage:	HC gerader Rücken kaschiert
Einband:	Gebunden
Autor:	Rubin, Boris
Hersteller:	Cambridge University Press
Maße:	240 x 161 x 39 mm
Von/Mit:	Boris Rubin
Erscheinungsdatum:	02.11.2015
Gewicht:	1,162 kg

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