Integral Geometry and Radon Transforms by Sigurdur Helgason

By Sigurdur Helgason

during this textual content, crucial geometry bargains with Radon’s challenge of representing a functionality on a manifold when it comes to its integrals over convinced submanifolds—hence the time period the Radon rework. Examples and far-reaching generalizations result in primary difficulties reminiscent of: (i) injectivity, (ii) inversion formulation, (iii) aid questions, (iv) purposes (e.g., to tomography, partial di  erential equations and workforce representations). For the case of the airplane, the inversion theorem and the help theorem have had significant functions in drugs via tomography and CAT scanning. whereas containing a few contemporary examine, the publication is geared toward starting graduate scholars for lecture room use or self-study. a couple of routines aspect to extra effects with documentation. From the studies: “Integral Geometry is an engaging sector, the place a variety of branches of arithmetic meet jointly. the contents of the booklet is targeted round the duality and double vibration, that is discovered in the course of the masterful therapy of quite a few examples. the ebook is written via a professional, who has made basic contributions to the area.” —Boris Rubin, Louisiana kingdom University

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