Integral Geometry and Representation Theory
eBook - PDF

Integral Geometry and Representation Theory

  1. 468 pages
  2. English
  3. PDF
  4. Available on iOS & Android
eBook - PDF

Integral Geometry and Representation Theory

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About This Book

Generalized Functions, Volume 5: Integral Geometry and Representation Theory is devoted to the theory of representations, focusing on the group of two-dimensional complex matrices of determinant one. This book emphasizes that the theory of representations is a good example of the use of algebraic and geometric methods in functional analysis, in which transformations are performed not on the points of a space, but on the functions defined on it. The topics discussed include Radon transform on a real affine space, integral transforms in the complex domain, and representations of the group of complex unimodular matrices in two dimensions. The properties of the Fourier transform on G, integral geometry in a space of constant curvature, harmonic analysis on spaces homogeneous with respect to the Lorentz Group, and invariance under translation and dilation are also described. This volume is suitable for mathematicians, specialists, and students learning integral geometry and representation theory.

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Yes, you can access Integral Geometry and Representation Theory by I. M. Gel'fand,M. I. Graev,N. Ya. Vilenkin in PDF and/or ePUB format, as well as other popular books in Mathematics & Mathematical Analysis. We have over one million books available in our catalogue for you to explore.

Information

Publisher
Academic Press
Year
2014
ISBN
9781483262253
Topic
Mathematics
Subtopic
Mathematical Analysis
Index
Mathematics

Table of contents

  1. Front Cover
  2. Integral Geometry and Representation Theory
  3. Copyright Page
  4. Table of Contents
  5. Translator's Note
  6. Foreword
  7. CHAPTER I. RADON TRANSFORM OF TEST FUNCTIONS AND GENERALIZED FUNCTIONS ON A REAL AFFINE SPACE
  8. CHAPTER II. INTEGRAL TRANSFORMS IN THE COMPLEX DOMAIN
  9. CHAPTER III. REPRESENTATIONS OF THE GROUP OF COMPLEX UNIMODULAR MATRICES IN TWO DIMENSIONS
  10. CHAPTER IV. HARMONIC ANALYSIS ON THE GROUP OF COMPLEX UNIMODULAR MATRICES IN TWO DIMENSIONS
  11. CHAPTER V. INTEGRAL GEOMETRY IN A SPACE OF CONSTANT CURVATURE
  12. CHAPTER VI. HARMONIC ANALYSIS ON SPACES HOMOGENEOUS WITH RESPECT TO THE LORENTZ GROUP
  13. CHAPTER VII. REPRESENTATIONS OF THE GROUP OF REAL UNIMODULAR MATRICES IN TWO DIMENSIONS
  14. NOTES AND REFERENCES TO THE LITERATURE
  15. BIBLIOGRAPHY
  16. Index