This book contains the proceedings of an AMS-IMS-SIAM Joint Summer Research Conference on Integral Geometry and Tomography, held in June 1989 at Humboldt State University in Arcata, California. The papers collected here represent current research in these two interrelated fields. The articles in pure mathematics range over such diverse areas as combinatorics, geometric inequalities, micro-local analysis, group theory, and harmonic analysis. The interplay between Lie group theory, geometry, harmonic analysis, and Radon transforms is well covered.The papers on tomography reflect current research on X-ray computed tomography, as well as radiation dose planning, radar, and partial differential equations. In addition to describing current research, this book provides a useful perspective on the interplay between the fields. For example, abstract theorems about Radon transforms are used to understand applied mathematics, while applied mathematics motivates some of the results in pure mathematics. Though directed at specialists in the field, the book would also be of interest to others who wish to understand current research in these areas and to witness how they relate to other branches of mathematics.
Admissible complexes for the combinatorial Radon transform. A Progress Report by E. D. Bolker, E. Grinberg, and J. P. S. Kung On generalized Radon transforms with unknown measures by Jan Paley-Wiener theorems on rank one symmetric spaces of noncompact type by W. O. Bray and D. C. Solmon Inversion of the X-ray transform: continuous vs.discrete by E. C. Tarabusi The mathematics and physics of radiation dose planning using X-rays by A. M. Cormack and E. T. Quinto The Radon transform and tensor products by L. Ehrenpreis An application of a multidimensional sampling theorem to computed tomography by A. Faridani The Radon transform for symmetric forms on real projective spaces by H. Goldschmidt Bi-invariant differential operators on the complex motion group and the range of the $d$-plane transform on $\mathbf C^n$ by F. B. Gonzalez Processes of flats induced by higher-dimensional processes II by P. R. Goodey and R. Howard Microlocal techniques in integral geometry by A. Greenleaf and G. Uhlmann The totally-geodesic Radon transform on constant curvature spaces by S. Helgason An application for a limited solid angle X-ray transform by S. H. Izen On a conjectured projection inequality of Petty by E. Lutwak A generalized Radon transform in wideband radar by P. Maass Summability and approximate reconstruction from Radon transform data by W. R. Madych An inverse problem for a transport equation and integral geometry by F. Natterer Invariant Radon transforms on a symmetric space by J. Orloff Nonuniqueness and the null space of the divergent beam X-ray transform by D. C. Solmon.