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.

Readership

Graduate students and research mathematicians interested in real analysis, integral geometry, and tomography.

Reviews

"Important and commendable ... Students fortunate enough to read and digest them will be exposed to a consistent, entertaining, and stimulatingly rich study, immensely suggestive, well researched, and intellectually appealing in their scholarly approach. Rarely do books meet such high aspirations, yet this one certainly does. All of the papers are consistently well-written by the most active and highly regarded researchers in the field, and promise to serve as a valuable reference source for many years to come."

-- Current Engineering Practice