ENGLISH

Integral Geometry and Radon Transforms

By Sigurdur Helgason (auth.)

Book information

Publisher
Springer-Verlag New York
Year
2011
ISBN
1441960546, 9781441960542, 9781441960559
DOI
10.1007/978-1-4419-6055-9
LCC
QA672 .H45 2011
Open Library ID
OL25101302M
Language
english
Format
PDF
Filesize
2 MB (2357436 bytes)
Edition
1
Pages
301\316
Time added
2011-06-04 13:46:07
Differential Geometry; Integral TransformsLie GroupsOperational Calculus; Global Analysis and Analysis

Description

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 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: “Integral 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.” —Boris Rubin, Louisiana State University

Similar books