Integral Geometry and Radon Transforms

Authors: Helgason, Sigurdur

  • Presents material accessible to advanced undergraduates
  • Contains the required expository material on Lie group theory
  • Features self-contained chapters with bibliographical notes, exercises, and further results (with documentation)
see more benefits

Buy this book

eBook $59.99
price for USA (gross)
  • ISBN 978-1-4419-6055-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $79.99
price for USA
  • ISBN 978-1-4419-6054-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $79.99
price for USA
  • ISBN 978-1-4899-9420-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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 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

About the authors

Dr. Sigurdur Helgason has authored or co-authered 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 well-written 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 X-ray technology and tomography. The nine-chapter volume devotes a chapter to these technologies and other applications. The book is largely self-contained, 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

    Helgason, Sigurdur

    Pages 1-62

  • A Duality in Integral Geometry

    Helgason, Sigurdur

    Pages 63-109

  • The Radon Transform on Two-Point Homogeneous Spaces

    Helgason, Sigurdur

    Pages 111-169

  • The X-Ray Transform on a Symmetric Space

    Helgason, Sigurdur

    Pages 171-184

  • Orbital Integrals and the Wave Operator for Isotropic Lorentz Spaces

    Helgason, Sigurdur

    Pages 185-208

Buy this book

eBook $59.99
price for USA (gross)
  • ISBN 978-1-4419-6055-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $79.99
price for USA
  • ISBN 978-1-4419-6054-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $79.99
price for USA
  • ISBN 978-1-4899-9420-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
Integral Geometry and Radon Transforms
Authors
Copyright
2011
Publisher
Springer-Verlag New York
Copyright Holder
Sigurdur Helgason
eBook ISBN
978-1-4419-6055-9
DOI
10.1007/978-1-4419-6055-9
Hardcover ISBN
978-1-4419-6054-2
Softcover ISBN
978-1-4899-9420-2
Edition Number
1
Number of Pages
XIII, 301
Topics