By Sigurdur Helgason

during this textual content, quintessential geometry bargains with Radon’s challenge of representing a functionality on a manifold by way of its integrals over definite submanifolds—hence the time period the Radon remodel. Examples and far-reaching generalizations bring about primary difficulties reminiscent of: (i) injectivity, (ii) inversion formulation, (iii) aid questions, (iv) functions (e.g., to tomography, partial di  erential equations and team representations). For the case of the airplane, the inversion theorem and the help theorem have had significant purposes in drugs via tomography and CAT scanning. whereas containing a few fresh learn, the publication is geared toward starting graduate scholars for school room use or self-study. a couple of workouts aspect to additional effects with documentation. From the studies: “Integral Geometry is an engaging zone, the place quite a few branches of arithmetic meet jointly. the contents of the e-book is targeted round the duality and double vibration, that is discovered throughout the masterful remedy of a number of examples. the ebook is written through a professional, who has made primary contributions to the area.” —Boris Rubin, Louisiana nation University

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