Integral Geometry and Radon Transforms
Springer-Verlag New York Inc.
978-1-4419-6054-2 (ISBN)
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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.
1.- The Radon Transformon on Rn 1.1- Introduction 1.2- The Radon Transform: The Support Theorem 1.3- The Inversion Formula: Injectivity Questions 1.4- The Plancherel Formula 1.5- Radon Transform of Distribution 1.6- Integration over d-planes: X-Ray Transforms 1.7- Applications 2.- A Duality in Integral Geometry 2.1- Homogeneous Spaces in Duality 2.2- The Radon Transform for the Double Fibration: Principal Problems 2.3- Orbital Integrals 2.4- Examples of Radon Transforms for Homogeneous Spaces in Duality 3.- The Radon Transform on Two-Point Homogeneous Spaces 3.1- Spaces of Constant Curvature: Inversion and Support Theorems 3.2- Compact Two-Point Homogeneous Spaces: Applications 3.3- Noncompact Two-Point Homogeneous Spaces 3.4- Support Theorems Relative to Horocycles 4.- The X-Ray Transform on a Symmetric Space 4.1- Compact Symmetric Spaces: Injectivity and Local Inversion: Support Theorem 4.2- Noncompact Symmetric Spaces: Global Inversion and General Support Theorem 4.3- Maximal Tori and Minimal Spheres in Compact Symmetric Spaces 5.- Orbital Integrals 5.1- Isotropic Spaces 5.2- Orbital Integrals 5.3- Generalized Riesz Potentials 5.4- Determination of a Function from its Integral over Lorentzian Spheres 5.5- Orbital Integrands and Huygens' Principle 6.- The Mean-Value Operator 6.1- An Injectivity Result 6.2- Ásgeirsson's Mean-Value Theorem Generalized 6.3- John's Indentities 7.- Fourier Transforms and Distribution: A Rapid Course 7.1-The Topology of Spaces D(Rn), E(Rn) and S(Rn) 7.2- Distribution 7.3- Convolutions 7.4- The Fourier Transform 7.5- Differential Operators with Constant Coefficients 7.6- Riesz Potentials 8.- Lie Transformation Groups and Differential Operators 8.1- Manifolds and Lie Groups 8.2- Lie Transformation Groups and Radon Transforms 9.- Bibliography 10.- Notational Conventions 11.- Index.
Erscheint lt. Verlag | 17.11.2010 |
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Zusatzinfo | 1 Tables, black and white; 72 Illustrations, black and white; XIII, 301 p. 72 illus. |
Verlagsort | New York, NY |
Sprache | englisch |
Maße | 155 x 235 mm |
Gewicht | 980 g |
Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
ISBN-10 | 1-4419-6054-6 / 1441960546 |
ISBN-13 | 978-1-4419-6054-2 / 9781441960542 |
Zustand | Neuware |
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