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Integral Geometry and Radon Transforms

  • Sigurdur Helgason

Table of contents

  1. Front Matter
    Pages 1-1
  2. Sigurdur Helgason
    Pages 1-62
  3. Sigurdur Helgason
    Pages 63-109
  4. Sigurdur Helgason
    Pages 111-169
  5. Sigurdur Helgason
    Pages 171-184
  6. Sigurdur Helgason
    Pages 209-219
  7. Sigurdur Helgason
    Pages 265-274
  8. Sigurdur Helgason
    Pages E1-E1
  9. Back Matter
    Pages 271-271

About this book

Introduction

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

Keywords

Homogeneous spaces in duality Manifolds and lie groups Radio astronomy Radon transform Spaces of constant curvature Topology of spaces X-ray tranform on symmetric spaces

Authors and affiliations

  • Sigurdur Helgason
    • 1
  1. 1., Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA

Bibliographic information