Integral geometry and radon transforms
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) inver...
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| Glavni autor: | |
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| Format: | Livre numérique |
| Jezik: | Anglais |
| Izdano: |
New York, NY :
Springer New York
[20..].
Cham : Springer Nature |
| Teme: | |
| Online pristup: | Accès sur la plateforme de l'éditeur Accès sur la plateforme de l'éditeur (Springer) Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Bilješka: |
Basé sur des cours donnés au MIT, Cambridge, Mass. en 1966 ainsi que sur les derniers développements publiés dans "the Radon transform" paru chez Birkhäuser en 1999 Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Integral geometry and Radon transforms, Sigurdur Helgason, New York, Springer, 2010, 1 vol. (XIII-301 p.), 978-1-441-96054-2 • Integral Geometry and Radon Transforms, Texte imprimé, 9781441960689 • Integral Geometry and Radon Transforms, Texte imprimé, 9781489994202 |
| Sažetak: | 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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| Opis djela: | Basé sur des cours donnés au MIT, Cambridge, Mass. en 1966 ainsi que sur les derniers développements publiés dans "the Radon transform" paru chez Birkhäuser en 1999 Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| ISBN: | 9781441960559 |
| Pristup: | Accès en ligne pour les établissements français bénéficiaires des licences nationales Accès soumis à abonnement pour tout autre établissement Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 |