Geometric Analysis and Integral Geometry

Geometric Analysis and Integral Geometry

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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.
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Product details

  • Paperback | 280 pages
  • 177.8 x 254 x 19.05mm | 417.3g
  • Providence, United States
  • English
  • 0821887386
  • 9780821887387

Table of contents

Historical articles:

Some personal remarks on the Radon transform by S. Helgason

On the life and work of S. Helgason by G. Olafsson and R. J. Stanton

Research and expository articles: Microlocal analysis of an ultrasound transform with circular source and receiver trajectories by G. Ambartsoumian, J. Boman, V. P. Krishnan, and E. T. Quinto

Cuspidal discrete series for projective hyperbolic spaces by N. B. Andersen and M. Flensted-Jensen

The Radon transform on $SO(3)$: Motivations, generalizations, discretization by S. Bernstein and I. Z. Pesenson

Atomic decompositions of Besov spaces related to symmetric cones by J. G. Christensen

A double fibration transform for complex projective space by M. Eastwood

Magnetic Schrodinger equation on compact symmetric spaces and the geodesic Radon transform of one forms by T. Kakehi

$F$-method for constructing equivariant differential operators by T. Kobayashi

Schiffer's conjecture, interior transmission eigenvalues and invisibility cloaking: Singular problem vs. nonsingular problem by H. Liu

Approximate reconstruction from circular and spherical mean Radon transform data by W. R. Madych

Analytic and group-theoretic aspects of the cosine transform by G. Olafsson, A. Pasquale, and B. Rubin

Quantization of linear algebra and its application to integral geometry by H. Oda and T. Oshima

Mean value theorems on symmetric spaces by F. Rouviere

Semyanistyi fractional integrals and Radon transforms by B. Rubin

Radon-Penrose transform between symmetric spaces by H. Sekiguchi

Principal series representations of infinite dimensional Lie groups, II: construction of induced representations by J. A. Wolf
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About Eric Todd Quinto

Eric Todd Quinto, Fulton Gonzalez, and Jens Gerlach Christensen, Tufts University, Medford, MA, USA
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