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Selected Topics in Integral Geometry
 
I. M. Gelfand Rutgers University, New Brunswick, NJ
S. G. Gindikin Rutgers University, New Brunswick, NJ
M. I. Graev Institute of System Studies, RAS, Moscow, Russia
Selected Topics in Integral Geometry
Hardcover ISBN:  978-0-8218-2932-5
Product Code:  MMONO/220
List Price: $165.00
MAA Member Price: $148.50
AMS Member Price: $132.00
eBook ISBN:  978-1-4704-4644-4
Product Code:  MMONO/220.E
List Price: $155.00
MAA Member Price: $139.50
AMS Member Price: $124.00
Hardcover ISBN:  978-0-8218-2932-5
eBook: ISBN:  978-1-4704-4644-4
Product Code:  MMONO/220.B
List Price: $320.00 $242.50
MAA Member Price: $288.00 $218.25
AMS Member Price: $256.00 $194.00
Selected Topics in Integral Geometry
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Selected Topics in Integral Geometry
I. M. Gelfand Rutgers University, New Brunswick, NJ
S. G. Gindikin Rutgers University, New Brunswick, NJ
M. I. Graev Institute of System Studies, RAS, Moscow, Russia
Hardcover ISBN:  978-0-8218-2932-5
Product Code:  MMONO/220
List Price: $165.00
MAA Member Price: $148.50
AMS Member Price: $132.00
eBook ISBN:  978-1-4704-4644-4
Product Code:  MMONO/220.E
List Price: $155.00
MAA Member Price: $139.50
AMS Member Price: $124.00
Hardcover ISBN:  978-0-8218-2932-5
eBook ISBN:  978-1-4704-4644-4
Product Code:  MMONO/220.B
List Price: $320.00 $242.50
MAA Member Price: $288.00 $218.25
AMS Member Price: $256.00 $194.00
  • Book Details
     
     
    Translations of Mathematical Monographs
    Volume: 2202003; 170 pp
    MSC: Primary 53; Secondary 42; 43; 44; 46; 60; 65; 92;

    The miracle of integral geometry is that it is often possible to recover a function on a manifold just from the knowledge of its integrals over certain submanifolds. The founding example is the Radon transform, introduced at the beginning of the 20th century. Since then, many other transforms were found, and the general theory was developed. Moreover, many important practical applications were discovered. The best known, but by no means the only one, being to medical tomography.

    This book is a general introduction to integral geometry, the first from this point of view for almost four decades. The authors, all leading experts in the field, represent one of the most influential schools in integral geometry. The book presents in detail basic examples of integral geometry problems, such as the Radon transform on the plane and in space, the John transform, the Minkowski–Funk transform, integral geometry on the hyperbolic plane and in the hyperbolic space, the horospherical transform and its relation to representations of \(SL(2,\mathbb C)\), integral geometry on quadrics, etc. The study of these examples allows the authors to explain important general topics of integral geometry, such as the Cavalieri conditions, local and nonlocal inversion formulas, and overdetermined problems in integral geometry. Many of the results in the book were obtained by the authors in the course of their career-long work in integral geometry.

    This book is suitable for graduate students and researchers working in integral geometry and its applications.

    Readership

    Graduate students and research mathematicians interested in integral geometry and applications.

  • Table of Contents
     
     
    • Chapters
    • Radon transform
    • John transform
    • Integral geometry and harmonic analysis on the hyperbolic plane and in the hyperbolic space
    • Integral geometry and harmonic analysis on the group ${G=SL(2,\mathbb C)}$
    • Integral geometry on quadrics
  • Additional Material
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 2202003; 170 pp
MSC: Primary 53; Secondary 42; 43; 44; 46; 60; 65; 92;

The miracle of integral geometry is that it is often possible to recover a function on a manifold just from the knowledge of its integrals over certain submanifolds. The founding example is the Radon transform, introduced at the beginning of the 20th century. Since then, many other transforms were found, and the general theory was developed. Moreover, many important practical applications were discovered. The best known, but by no means the only one, being to medical tomography.

This book is a general introduction to integral geometry, the first from this point of view for almost four decades. The authors, all leading experts in the field, represent one of the most influential schools in integral geometry. The book presents in detail basic examples of integral geometry problems, such as the Radon transform on the plane and in space, the John transform, the Minkowski–Funk transform, integral geometry on the hyperbolic plane and in the hyperbolic space, the horospherical transform and its relation to representations of \(SL(2,\mathbb C)\), integral geometry on quadrics, etc. The study of these examples allows the authors to explain important general topics of integral geometry, such as the Cavalieri conditions, local and nonlocal inversion formulas, and overdetermined problems in integral geometry. Many of the results in the book were obtained by the authors in the course of their career-long work in integral geometry.

This book is suitable for graduate students and researchers working in integral geometry and its applications.

Readership

Graduate students and research mathematicians interested in integral geometry and applications.

  • Chapters
  • Radon transform
  • John transform
  • Integral geometry and harmonic analysis on the hyperbolic plane and in the hyperbolic space
  • Integral geometry and harmonic analysis on the group ${G=SL(2,\mathbb C)}$
  • Integral geometry on quadrics
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.