Integral Geometry and Radon Transforms

Sigurdur Helgason

ISBN 10: 1441960546 / ISBN 13: 9781441960542

Editore: Springer New York, Springer US Nov 2010, 2010

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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.

Codice articolo 9781441960542

Dati bibliografici

• Titolo: Integral Geometry and Radon Transforms
• Editore: Springer New York, Springer US Nov 2010
• Data di pubblicazione: 2010
• Lingua: Inglese
• ISBN 10: 1441960546
• ISBN 13: 9781441960542
• Rilegatura: Buch
• Condizione: Neu
• Dimensioni: 241 L x 160 A x 23 P (millimetri) 241 millimetri di larghezza per 160 millimetri di altezza per 23 millimetri di profondità
• Peso: 641 grammi

Descrizione articolo

Riassunto

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

Informazioni sull?autore

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.