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Catalogue Information
Field name	Details
Dewey Class	516.36
Title	Integral Geometry and Radon Transforms ([Ebook]) / by Sigurdur Helgason.
Author	Helgason, Sigurdur, , 1927-
Other name(s)	SpringerLink (Online service)
Publication	New York, NY : Springer , 2011.
Physical Details	XIII, 301 pages: 28 illus. : online resource.
ISBN	9781441960559
Summary Note	In this text, integral geometry deals with Radonâs problem of representing a function on a manifold in terms of its integrals over certain submanifoldsâhence the term the Radon transform. Examples and far-reaching generalizations lead to fundamental problems such as: (i) injectivity, (ii) inversion formulas, (iii) support questions, (iv) applications (e.g., to tomography, partial differential equations and group representations). For the case of the plane, the inversion theorem and the support theorem have had major applications in medicine through tomography and CAT scanning. While containing some recent research, the book is aimed at beginning graduate students for classroom use or self-study. A number of exercises point to further results with documentation. From the reviews: âIntegral Geometry is a fascinating area, where numerous branches of mathematics meet together. The contents of the book is concentrated around the duality and double fibration, which is realized through the masterful treatment of a variety of examples. The book is written by an expert, who has made fundamental contributions to the area.â âBoris Rubin, Louisiana State University:
Contents note	The Radon Transformon Rn -- A Duality in Integral Geometry -- The Radon Transform on Two-Point Homogeneous Spaces -- The X-Ray Transform on a Symmetric Space -- Orbital Integrals -- The Mean-Value Operator -- Fourier Transforms and Distribution: A Rapid Course -- Lie Transformation Groups and Differential Operators -- Bibliography -- Notational Conventions -- Index.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	http://dx.doi.org/10.1007/978-1-4419-6055-9
Links to Related Works	Subject References: Differential Geometry . Global analysis . Global differential geometry . Integral geometry . Integral transforms . Topological groups . Topological groups, Lie groups . Authors: Helgason, Sigurdur, 1927- . Corporate Authors: SpringerLink (Online service) . Classification: 516.36 . 516.36 (DDC 23) .

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Integral Geometry and Radon Transforms

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