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Geometric Analysis and Integral Geometry
 
Edited by: Eric Todd Quinto Tufts University, Medford, MA
Fulton Gonzalez Tufts University, Medford, MA
Jens Gerlach Christensen Tufts University, Medford, MA
Geometric Analysis and Integral Geometry
Softcover ISBN:  978-0-8218-8738-7
Product Code:  CONM/598
List Price: $130.00
MAA Member Price: $117.00
AMS Member Price: $104.00
eBook ISBN:  978-1-4704-1026-1
Product Code:  CONM/598.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-0-8218-8738-7
eBook: ISBN:  978-1-4704-1026-1
Product Code:  CONM/598.B
List Price: $255.00 $192.50
MAA Member Price: $229.50 $173.25
AMS Member Price: $204.00 $154.00
Geometric Analysis and Integral Geometry
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Geometric Analysis and Integral Geometry
Edited by: Eric Todd Quinto Tufts University, Medford, MA
Fulton Gonzalez Tufts University, Medford, MA
Jens Gerlach Christensen Tufts University, Medford, MA
Softcover ISBN:  978-0-8218-8738-7
Product Code:  CONM/598
List Price: $130.00
MAA Member Price: $117.00
AMS Member Price: $104.00
eBook ISBN:  978-1-4704-1026-1
Product Code:  CONM/598.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-0-8218-8738-7
eBook ISBN:  978-1-4704-1026-1
Product Code:  CONM/598.B
List Price: $255.00 $192.50
MAA Member Price: $229.50 $173.25
AMS Member Price: $204.00 $154.00
  • Book Details
     
     
    Contemporary Mathematics
    Volume: 5982013; 280 pp
    MSC: Primary 22; 43; 44; 45; 92; Secondary 32; 35; 65;

    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.

    Readership

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

  • Table of Contents
     
     
    • Historical articles
    • Sigurdur Helgason — Some personal remarks on the Radon transform
    • G. Ólafsson and R. J. Stanton — On the Life and Work of S. Helgason
    • Rsearch 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
    • 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
  • Additional Material
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 5982013; 280 pp
MSC: Primary 22; 43; 44; 45; 92; Secondary 32; 35; 65;

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.

Readership

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

  • Historical articles
  • Sigurdur Helgason — Some personal remarks on the Radon transform
  • G. Ólafsson and R. J. Stanton — On the Life and Work of S. Helgason
  • Rsearch 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
  • 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
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.