Senin, 21 Juli 2014

? Download Ebook The Radon Transform (Progress in Mathematics) (Vol 5), by Sigurdur Helgason

Download Ebook The Radon Transform (Progress in Mathematics) (Vol 5), by Sigurdur Helgason

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The Radon Transform (Progress in Mathematics) (Vol 5), by Sigurdur Helgason

The Radon Transform (Progress in Mathematics) (Vol 5), by Sigurdur Helgason



The Radon Transform (Progress in Mathematics) (Vol 5), by Sigurdur Helgason

Download Ebook The Radon Transform (Progress in Mathematics) (Vol 5), by Sigurdur Helgason

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The Radon Transform (Progress in Mathematics) (Vol 5), by Sigurdur Helgason

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.

  • Sales Rank: #2687451 in Books
  • Brand: Brand: Birkhäuser
  • Published on: 1999-08-01
  • Original language: English
  • Number of items: 1
  • Dimensions: 9.21" h x .50" w x 6.14" l, .90 pounds
  • Binding: Hardcover
  • 193 pages
Features
  • Used Book in Good Condition

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.

Most helpful customer reviews

5 of 7 people found the following review helpful.
Not Exactly
By Jim Curry
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.

7 of 8 people found the following review helpful.
Theory
By A Customer
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.

4 of 7 people found the following review helpful.
a page-turner
By Michele
I love all the novels of this author. This one was even better!

"The Radon transform" is the story of a secret company living in the boundary of society. Their effect on the world is hidden, as we can only see its total impact on hyperplanes. All the pitch of the book is to uncover the actual organisation of this guild.

It's a book I would advise to any avid reader of the thrillers of Schwartz, Bourbaki or the saga of Hormander.

See all 3 customer reviews...

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