 Presents material accessible to advanced undergraduates
 Contains the required expository material on Lie group theory
 Features selfcontained chapters with bibliographical notes, exercises, and further results (with documentation)
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 About this Textbook

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 farreaching 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 selfstudy. 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
 About the authors

Dr. Sigurdur Helgason has authored or coauthered 9 books and 94 papers. He has received numerous honors and awards, including the Steele Prize, awarded by the American Mathematical Society in 1988. He has been a professor at MIT since 1960.
 Reviews

From the reviews:
“Beginning graduate students and interested nonspecialists will gain from the book because of its clear exposition and comprehensive nature. Practitioners of integral geometry will find it a valuable reference with complete and clear proofs as well as specialized items of interest … . This book is a wellwritten and beautiful introduction to integral geometry from the perspective of group actions. It has valuable thought provoking exercises. … It should be read by anyone who would like to learn more about integral geometry.” (Fulton Gonzalez and Eric Todd Quinto, Bulletin of the American Mathematical Society, Vol. 50 (4), October, 2013)
“This specialist book in the field of geometric analysis is intended for graduate students and professionals. … The field has several applications including medical Xray technology and tomography. The ninechapter volume devotes a chapter to these technologies and other applications. The book is largely selfcontained, and includes a chapter at the end with necessary background material … . The volume includes a substantial bibliography, and each chapter concludes with bibliographic notes. Summing Up: Recommended. Graduate students and above.” (D. Z. Spicer, Choice, Vol. 48 (11), August, 2011)
“Integral Geometry and Radon Transforms is truly a pedagogical contribution by a master in this field, aiming at providing proper background – and then some – for entry into real work on the topics he brings into the spotlight. … every page is filled with serious mathematics, and Helgason provides a lot of commentary and references that ought to be pursued by those wishing to enter the field. It is a marvelous example of fine scholarship.” (Michael Berg, The Mathematical Association of America, January, 2011)
“The book under review is devoted to integral operators of geometric nature. The monograph deals with the problem of representing a function on a manifold in terms of its integrals over certain submanifolds – hence the term Radon transform. … The book will be of interest for both students and specialists in integral geometry, analysis on homogeneous spaces and partial differential equations. It may serve as a source for further research in the area.” (Valery Vladimirovich Volchkov, Zentralblatt MATH, Vol. 1210, 2011)
 Table of contents (10 chapters)


The Radon Transform on R n
Pages 162

A Duality in Integral Geometry
Pages 63109

The Radon Transform on TwoPoint Homogeneous Spaces
Pages 111169

The XRay Transform on a Symmetric Space
Pages 171184

Orbital Integrals and the Wave Operator for Isotropic Lorentz Spaces
Pages 185208

Table of contents (10 chapters)
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Bibliographic Information
 Bibliographic Information

 Book Title
 Integral Geometry and Radon Transforms
 Authors

 Sigurdur Helgason
 Copyright
 2011
 Publisher
 SpringerVerlag New York
 Copyright Holder
 Sigurdur Helgason
 eBook ISBN
 9781441960559
 DOI
 10.1007/9781441960559
 Hardcover ISBN
 9781441960542
 Softcover ISBN
 9781489994202
 Edition Number
 1
 Number of Pages
 XIII, 301
 Topics