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Sinopsis
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 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 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
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Acerca del autor
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.
De la contraportada
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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- EditorialSpringer
- Año de publicación2010
- ISBN 10 1441960546
- ISBN 13 9781441960542
- EncuadernaciónTapa dura
- IdiomaInglés
- Número de páginas316
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Integral Geometry and Radon Transforms
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Integral Geometry and Radon Transforms
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Buch. Condición: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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 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 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 316 pp. Englisch. Nº de ref. del artículo: 9781441960542
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Integral Geometry and Radon Transforms
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Gebunden. Condición: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Presents material accessible to advanced undergraduatesContains the required expository material on Lie group theoryFeatures self-contained chapters with bibliographical notes, exercises, and further results (with documentation)Dr. . Nº de ref. del artículo: 4175963
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Buch. Condición: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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 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 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. Nº de ref. del artículo: 9781441960542
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Integral Geometry and Radon Transforms
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Buch. Condición: Neu. Neuware -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 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 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 UniversitySpringer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 316 pp. Englisch. Nº de ref. del artículo: 9781441960542
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Integral Geometry and Radon Transforms
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