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 di erential equations and group representations). For the case of the plane, the inversion theorem and the support theorem have had major applications in medicinethrough 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 thereviews: “Integral Geometry is a fascinating area, where numerous branches ofmathematics meet together. the contents of the book is concentrated around the duality and double vibration, 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 Accessible to advanced undergraduates. New content on lie group theory accessible to anyone familiar with manifolds. Self-contained chapters each with bibliographical notes and practice exercises. INDICE: 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.
- ISBN: 978-1-4419-6054-2
- Editorial: Springer New York
- Encuadernacion: Cartoné
- Páginas: 301
- Fecha Publicación: 17/11/2010
- Nº Volúmenes: 1
- Idioma: Inglés