The Radon Transform (Progress in Mathematics) (Vol 5) [Hardcover]

Sigurdur Helgason (Author)

Book Description

Publication Date: August 1, 1999 | ISBN-10: 0817641092 | ISBN-13: 978-0817641092 | Edition: 2nd

The Radon transform is an important topic in integral geometry which deals with the problem of expressing a function on a manifold in terms of its integrals over certain submanifolds. Solutions to such problems have a wide range of applications, namely to partial differential equations, group representations, X-ray technology, nuclear magnetic resonance scanning, and tomography. This second edition, significantly expanded and updated, presents new material taking into account some of the progress made in the field since 1980. Aimed at beginning graduate students, this monograph will be useful in the classroom or as a resource for self-study. Readers will find here an accessible introduction to Radon transform theory, an elegant topic in integral geometry.

Editorial Reviews

Review

"This is the second edition of the famous book by Sigurdur Helgason which has been updated in accordance with recent new results in this area. The list of references and bibliographical notes have been essentially extended. Many examples with explicit inversion formulas and range theorems have been added, and the group-theoretic viewpoint is emphasized... [the] author adds a new chapter, Chapter 5, which contains useful information about Fourier transforms, distributions and Riesz potentials. The second edition preserves the nice introductory flavor of the first one. The book will be highly appreciated by the mathematical community." --Mathematical Reviews (on the second edition) "...well-written and a pleasure to read...provides clear explanations and illustrative figures... Every important point receives a clear proof. The author puts a great deal of effort into motivating his readers. The chapters have been updated by the inclusion of some applications and by giving indications in bibliographical notes of some recent developments... [an] excellent introduction to an area of mathematics which seems to have attracted much new interest...highly recommendable...for graduate students... and researchers." --ZAA (on the second edition) "Until now the subject [The Radon transform] has lacked anything approaching a systematic exposition aimed at beginners. Publication of the present volume...by one of the chief contributors to the modern theory of the Radon transform, is thus…timely and welcome...Helgason's notes provide the most agreeable introduction to the Radon transform currently available. [A] reader will be charmed by the interplay of geometry and analysis exhibited here and reassured by the explicit nature of the formulas obtained. [Chapter 3] is the heart of the second half of the book and, on balance, provides an admirable introit to a branch of analysis which deserves to be known by a wider public." --SIAM Review (on the first edition)    

From the Back Cover

The Radon transform is an important topic in integral geometry which deals with the problem of expressing a function on a manifold in terms of its integrals over certain submanifolds. Solutions to such problems have a wide range of applications, namely to partial differential equations, group representations, X-ray technology, nuclear magnetic resonance scanning, and tomography. This second edition, significantly expanded and updated, presents new material taking into account some of the progress made in the field since 1980. The first chapter introduces the Radon transform and presents new material on the d-plane transform and applications to the wave equation. Chapter 2 places the Radon transform in a general framework of integral geometry known as a double fibration of a homogeneous space. Several significant examples are developed in detail. Two subsequent chapters treat some specific examples of generalized Radon transforms, for examples, antipodal manifold in compact 2-points homogeneous spaces, and orbital integrals in isotropic Lorentzian manifolds. A final chapter deals with Fourier transforms and distributions, developing all the tools needed in the work. Aimed at beginning graduate students, this monograph will be useful in the classroom or as a resource for self-study. Readers will find here an accessible introduction to Radon transform theory, an elegant topic in integral geometry.

Product Details

• Hardcover: 200 pages
• Publisher: Birkhäuser Boston; 2nd edition (August 1, 1999)
• Language: English
• ISBN-10: 0817641092
• ISBN-13: 978-0817641092
• Product Dimensions: 9.3 x 6.4 x 0.8 inches
• Shipping Weight: 14.4 ounces (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #2,300,334 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

5 of 6 people found the following review helpful:

5.0 out of 5 stars Theory, March 12, 2004

By A Customer

This review is from: The Radon Transform (Progress in Mathematics) (Vol 5) (Hardcover)

I saw a previous (1st) edition of this book in my college library. It's too theoretical for engineers--useless for engineers. It's written for mathematicians. I thought this would help since u can't see what's inside online.

3 of 5 people found the following review helpful:

5.0 out of 5 stars Not Exactly, February 7, 2009

By 

Jim Curry (MT) - See all my reviews
(VINE VOICE)   

This review is from: The Radon Transform (Progress in Mathematics) (Vol 5) (Hardcover)

Everything Helgason writes is incisive, insightful, and meticulously correct. I object a little bit with the only review I found at this location. It says that this book is not very useful for engineers. That depends a lot on the engineer. As a student at Caltech, I had several professors who were quite high level engineers. These were not people confused somehow by higher mathematics and technology. They were people who fully mastered the language of mathematics and went beyond the language itself to speak it in useful technological ways. For engineers and scientists with "horsepower," everything Helgason writes provides insight that is difficult to find elsewhere. The question isn't whether it is practical learning or not. It certainly is deeply practical. The question is whether the engineer in question (the reader) has the big intellectual engine required to digest and use it. There will inevitably be full, tenured professors at lesser institutions (I know many of them) who would consider this to be impractical learning. That view will not hold water at the top schools.