Quinto E.T., Gonzalez F., Christensen J.G. (Eds.) Geometric Analysis and Integral Geometry

American Mathematical Society, USA, 2013. — 298 p. — (Contemporary mathematics 598) — ISBN: 0821887386.This volume contains the proceedings of the AMS Special Session on Radon Transforms and Geometric Analysis, in honour 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 Olafsson 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.Historical Articles
Some Personal Remarks on the Radon Transform
On the Life and Work of S. Helgason
Research and Expository Articles
Microlocal Analysis of an Ultrasound Transform with Circular Source and Receiver Trajectories
Cuspidal discrete series for projective hyperbolic spaces
The Radon transform on SO(3): motivations, generalizations, discretization
Atomic decompositions of Besov spaces related to symmetric cones
A double fibration transform for complex projective space
Magnetic Schr¨odinger equation on compact symmetric spaces and the geodesic. Radon transform of one forms
F-method for constructing equivariant differential operators
Schiffer’s Conjecture, Interior Transmission Eigenvalues and Invisibility Cloaking: Singular Problem vs. Nonsingular Problem
Approximate Reconstruction from Circular and Spherical Mean Radon Transform Data
Analytic and Group-Theoretic Aspects of the Cosine Transform
Quantization of linear algebra and its application to integral geometry
Mean value theorems on symmetric spaces
Semyanistyi fractional integrals and Radon transforms
Radon-Penrose transform between symmetric spaces
Principal series representations of infinite dimensional Lie groups, II: Construction of induced representations