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Generalized functions. Volume 5, Integral geometry and representation theory /
Integral Geometry and Representation Theory.
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , , |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés Ruso |
| Publicado: |
New York :
Academic Press,
1966.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Front Cover; Integral Geometry and Representation Theory; Copyright Page; Translator's Note; Foreword; Table of Contents; CHAPTER I. RADON TRANSFORM OF TEST FUNCTIONS AND GENERALIZED FUNCTIONSON A REAL AFFINE SPACE; 1. The Radon Transform on a Real Affine Space; 2. The Radon Transform of Generalized Functions; 3. Radon Transforms of Some Particular Generalized Functions; 4. Summary of Radon Transform Formulas; CHAPTER II. INTEGRAL TRANSFORMS IN THECOMPLEX DOMAIN; 1. Line Complexes in a Space of Three Complex Dimensionsand Related Integral Transforms
- 2. Integral Geometry on a Quadratic Surface in a Space of Four Complex Dimensions3. The Radon Transform in the Complex Domain; CHAPTER III. REPRESENTATIONS OF THE GROUP OF COMPLEX UNIMODULAR MATRICESIN TWO DIMENSIONS; 1. The Group of Complex Unimodular Matricesin Two Dimensions and Some of Its Realizations; 2. Representations of the Lorentz GroupActing on Homogeneous Functions of Two Complex Variables; 3. Summary of Basic Results concerning Representations on Dx; 4. Invariant Bilinear Functionals; 5. Equivalence of Representations of G; 6. Unitary Representations of G
- CHAPTER IV. HARMONIC ANALYSIS ON THE GROUP OF COMPLEX UNIMODULAR MATRICESIN TWO DIMENSIONS1. Definition of the Fourier Transform on a Group. Statement of the Problems and Summary of the Results; 2, Properties of the Fourier Transform on G; 3. Inverse Fourier Transform and Plancherel's Theorem for G; 4. Differential Operators on G; 5. The Paley-Wiener Theorem for the Fourier Transform on G; CHAPTER V. INTEGRAL GEOMETRYIN A SPACE OF CONSTANT CURVATURE; 1. Spaces of ConstantCurvature; 2. Integral Transform Associated with Horospheresin a Lobachevskian Space
- 3. Integral Transform Associated with Horospheresin an Imaginary Lobachevskian SpaceCHAPTER VI. HARMONIC ANALYSIS ON SPACES HOMOGENEOUS WITH RESPECT TO THELORENTZ GROUP; 1. Homogeneous Spaces and the Associated Representationsof the Lorentz Group; 2. Representations of the Lorentz Group Associated with the Complex Affine Plane and with the Cone, and Their Irreducible Components; 3. Decomposition of the Representation of the Lorentz GroupAssociated with Lobachevskian Space; 4. Decomposition of the Representation of the Lorentz GroupAssociated with Imaginary Lobachevskian Space
- 5. Integral Geometry and Harmonic Analysis on the Point Pairs on the Complex Projective LineCHAPTER VII. REPRESENTATIONS OF THE GROUP OF REAL UNIMODULAR MATRICESIN TWO DIMENSIONS; 1. Representations of the Real Unimodular Matrices in Two Dimensions Acting on Homogeneous Functionsof Two Real Variables; 2. Summary of the Basic Results concerningRepresentations on Dx; 3. Invariant Bilinear Functionals; 4. Equivalence of Two Representations; 5. Unitary Representations of G; NOTES AND REFERENCESTO THE LITERATURE; BIBLIOGRAPHY; Index