Integral Geometry and Radon Transforms [recurso electrónico] / by Sigurdur Helgason.
Tipo de material: TextoEditor: New York, NY : Springer New York, 2011Descripción: XIII, 301 p. online resourceTipo de contenido: text Tipo de medio: computer Tipo de portador: online resourceISBN: 9781441960559Tema(s): Mathematics | Topological Groups | Global analysis | Integral Transforms | Global differential geometry | Mathematics | Differential Geometry | Integral Transforms, Operational Calculus | Global Analysis and Analysis on Manifolds | Topological Groups, Lie GroupsFormatos físicos adicionales: Printed edition:: Sin títuloClasificación CDD: 516.36 Clasificación LoC:QA641-670Recursos en línea: Libro electrónicoTipo de ítem | Biblioteca actual | Colección | Signatura | Copia número | Estado | Fecha de vencimiento | Código de barras |
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Libro Electrónico | Biblioteca Electrónica | Colección de Libros Electrónicos | QA641 -670 (Browse shelf(Abre debajo)) | 1 | No para préstamo | 371570-2001 |
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QA641 -670 Modern Differential Geometry in Gauge Theories | QA641 -670 Riemannian Geometry of Contact and Symplectic Manifolds | QA641 -670 CR Submanifolds of Complex Projective Space | QA641 -670 Integral Geometry and Radon Transforms | QA641 -670 Topics in Extrinsic Geometry of Codimension-One Foliations | QA641 -670 Elementary Differential Geometry | QA641 -670 Topics in Physical Mathematics |
The Radon Transformon Rn -- A Duality in Integral Geometry -- The Radon Transform on Two-Point Homogeneous Spaces -- The X-Ray Transform on a Symmetric Space -- Orbital Integrals -- The Mean-Value Operator -- Fourier Transforms and Distribution: A Rapid Course -- Lie Transformation Groups and Differential Operators -- Bibliography -- Notational Conventions -- Index.
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
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