The Radon transform is an important topic in integral geometry which deals with the problem of expressing a function on a manifold in terms of its integrals over certain submanifolds. Solutions to such problems have a wide range of applications, namely to partial differential equations, group representations, Xray technology, nuclear magnetic resonance scanning, and tomography. This second edition, significantly expanded and updated, presents new material taking into account some of the progress made in the field since 1980. The first chapter introduces the Radon transform and presents new material on the dplane transform and applications to the wave equation. Chapter 2 places the Radon transform in a general framework of integral geometry known as a double fibration of a homogeneous space. Several significant examples are developed in detail. Two subsequent chapters treat some specific examples of generalized Radon transforms, for examples, antipodal manifold in compact 2points homogeneous spaces, and orbital integrals in isotropic Lorentzian manifolds. A final chapter deals with Fourier transforms and distributions, developing all the tools needed in the work. Aimed at beginning graduate students, this monograph will be useful in the classroom or as a resource for selfstudy. Readers will find here an accessible introduction to Radon transform theory, an elegant topic in integral geometry.
About Sigurdur Helgason
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Author  :  Sigurdur Helgason 
Publisher  :  Birkhauser Verlag AG 
Data Published  :  01 August 1999 
ISBN  :  0817641092 
EAN  :  9780817641092 
Format Book  :  PDF, Epub, DOCx, TXT 
Number of Pages  :  212 pages 
Age +  :  15 years 
Language  :  English 
Rating  : 
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