Geometric Analysis and Integral Geometry
About this Title
Eric Todd Quinto, Tufts University, Medford, MA, Fulton Gonzalez, Tufts University, Medford, MA and Jens Gerlach Christensen, Tufts University, Medford, MA, Editors
Publication: Contemporary Mathematics
Publication Year: 2013; Volume 598
ISBNs: 978-0-8218-8738-7 (print); 978-1-4704-1026-1 (online)
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.
Table of Contents
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- Sigurdur Helgason – Some personal remarks on the Radon transform
- G. Ólafsson and R. J. Stanton – On the Life and Work of S. Helgason
- G. Ambartsoumian, J. Boman, V. P. Krishnan and E. T. Quinto – Microlocal analysis of an ultrasound transform with circular source and receiver trajectories
- Nils Byrial Andersen and Mogens Flensted–Jensen – Cuspidal discrete series for projective hyperbolic spaces
- Swanhild Bernstein and Isaac Z. Pesenson – The Radon transform on $SO(3)$: motivations, generalizations, discretization
- Jens Gerlach Christensen – Atomic decompositions of Besov spaces related to symmetric cones
- Michael Eastwood – A double fibration transform for complex projective space
- Tomoyuki Kakehi – Magnetic Schrödinger equation on compact symmetric spaces and the geodesic Radon transform of one forms
- Toshiyuki Kobayashi – $F$-method for constructing equivariant differential operators
- Hongyu 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
- Hiroshi Oda and Toshio Oshima – Quantization of linear algebra and its application to integral geometry
- François Rouvière – Mean value theorems on symmetric spaces
- B. Rubin – Semyanistyi fractional integrals and Radon transforms
- Hideko Sekiguchi – Radon–Penrose transform between symmetric spaces
- Joseph A. Wolf – Principal series representations of infinite dimensional Lie groups, II: Construction of induced representations