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Geometric Analysis and Integral Geometry
Edited by: Eric Todd Quinto, Fulton Gonzalez, and Jens Gerlach Christensen, Tufts University, Medford, MA
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Contemporary Mathematics
2013; 280 pp; softcover
Volume: 598
ISBN-10: 0-8218-8738-6
ISBN-13: 978-0-8218-8738-7
List Price: US$100 Member Price: US$80
Order Code: CONM/598

This volume contains the proceedings of the AMS Special Session on Radon Transforms and Geometric Analysis, in honor of Sigurdur Helgason's 85th Birthday, held from January 4-7, 2012, in Boston, MA, and the Tufts University Workshop on Geometric Analysis on Euclidean and Homogeneous Spaces, held from January 8-9, 2012, in Medford, MA.

This volume provides an historical overview of several decades in integral geometry and geometric analysis as well as recent advances in these fields and closely related areas. It contains several articles focusing on the mathematical work of Sigurdur Helgason, including an overview of his research by Gestur Ólafsson and Robert Stanton. The first article in the volume contains Helgason's own reminiscences about the development of the group-theoretical aspects of the Radon transform and its relation to geometric analysis. Other contributions cover Radon transforms, harmonic analysis, Penrose transforms, representation theory, wavelets, partial differential operators on groups, and inverse problems in tomography and cloaking that are related to integral geometry.

Many articles contain both an overview of their respective fields as well as new research results. The volume will therefore appeal to experienced researchers as well as a younger generation of mathematicians. With a good blend of pure and applied topics the volume will be a valuable source for interdisciplinary research.

Graduate students and researchers interested in integral geometry, representation theory, harmonic and geometric analysis.

Historical articles
• S. Helgason -- Some personal remarks on the Radon transform
• G. Ólafsson and R. J. Stanton -- On the life and work of S. Helgason
Research and expository articles
• G. Ambartsoumian, J. Boman, V. P. Krishnan, and E. T. Quinto -- Microlocal analysis of an ultrasound transform with circular source and receiver trajectories
• N. B. Andersen and M. Flensted-Jensen -- Cuspidal discrete series for projective hyperbolic spaces
• S. Bernstein and I. Z. Pesenson -- The Radon transform on $$SO(3)$$: Motivations, generalizations, discretization
• J. G. Christensen -- Atomic decompositions of Besov spaces related to symmetric cones
• M. Eastwood -- A double fibration transform for complex projective space
• T. Kakehi -- Magnetic Schrödinger equation on compact symmetric spaces and the geodesic Radon transform of one forms
• T. Kobayashi -- $$F$$-method for constructing equivariant differential operators
• H. Liu -- Schiffer's conjecture, interior transmission eigenvalues and invisibility cloaking: Singular problem vs. nonsingular problem
• W. R. Madych -- Approximate reconstruction from circular and spherical mean Radon transform data
• G. Ólafsson, A. Pasquale, and B. Rubin -- Analytic and group-theoretic aspects of the cosine transform
• H. Oda and T. Oshima -- Quantization of linear algebra and its application to integral geometry
• F. Rouvière -- Mean value theorems on symmetric spaces
• B. Rubin -- Semyanistyi fractional integrals and Radon transforms
• H. Sekiguchi -- Radon-Penrose transform between symmetric spaces
• J. A. Wolf -- Principal series representations of infinite dimensional Lie groups, II: construction of induced representations