Integral Geometry and Radon Transforms 2011th Edition by Sigurdur Helgason (PDF)

Description

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

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This book is a welcome addition to the many books and papers the author has published on the subject of Radon Transforms and in particular for homogeneous spaces in duality. Like the author’s other books on the subject, this book is very well written and is attempted to be self-contained; it can be used as a text book in an advanced graduate level mathematic class. In addition the many updates based on recently published results on the subject, new and improved proofs to some old results are given in this book. Some of the new approaches used in these proofs could possibly be applied to the study of other examples of homogeneous spaces in duality involving symmetric spaces of ranks higher than one. It is also refreshing to find detailed discussions with complete solutions to the some of the critical engineering problems encountered in the application of Radon transforms to tomography in X-ray technology, a Nobel Prize winning discovery, in a book on theoretical mathematics.

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