This volume consists of a collection of papers that brings together fundamental research in Radon transforms, integral geometry, and tomography. It grew out of the Special Session at a Sectional Meeting of the American Mathematical Society in 2004. The book contains very recent work of some of the top researchers in the field. The articles in the book deal with the determination of properties of functions on a manifold by integral theoretic methods, or by determining the geometric structure of subsets of a manifold by analytic methods. Of particular concern are ways of reconstructing an unknown function from some of its projections.Radon transforms were developed at the beginning of the twentieth century by researchers who were motivated by problems in differential geometry, mathematical physics, and partial differential equations. Later, medical applications of these transforms produced breakthroughs in imaging technology that resulted in the 1979 Nobel Prize in Physiology and Medicine for the development of computerized tomography. Today the subject boasts substantial cross-disciplinary interactions, both in pure and applied mathematics as well as medicine, engineering, biology, physics, geosciences, and industrial testing. Therefore, this volume should be of interest to a wide spectrum of researchers both in mathematics and in other fields.
Remarks on stationary sets for the wave equation by M. L. Agranovsky and E. T. Quinto Network tomography by C. Berenstein, F. Gavilanez, and J. Baras On stable inversion of the attenuated Radon transform with half data by J. Boman Wavelet sets without groups by M. Dobrescu and G. Olafsson The Radon transform for functions defined on planes by L. Ehrenpreis The modified wave equation on the sphere by F. B. Gonzalez and J. Zhang Analysis of a family of exact inversion formulas for cone beam computer tomography by A. Katsevich and A. Zamyatin The $k$-plane transform and Riesz potentials by A. Markoe The composite cosine transform on the Stiefel manifold and generalized zeta integrals by E. Ournycheva and B. Rubin Frames for spaces of Paley-Wiener functions on Riemannian manifolds by I. Pesenson Properties of the stationary sets for the wave equation by J. Rennie.