eBook ISBN:  9780821876534 
Product Code:  CONM/63.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
eBook ISBN:  9780821876534 
Product Code:  CONM/63.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 

Book DetailsContemporary MathematicsVolume: 63; 1987; 350 ppMSC: Primary 53; Secondary 22
The topic of integral geometry is not as well known as its counterpart, differential geometry. However, research in integral geometry has indicated that this field may yield as equally deep insights as differential geometry has into the global and local nature of manifolds and the functions on them. In 1984, an AMSIMSSIAM joint summer research conference on integral geometry was held at Bowdoin College. This volume consists of papers presented there.
The papers range from purely expository to quite technical and represent a good survey of contemporary work in integral geometry. Three major areas are covered: the classical problems of computing geometric invariants by statistical averaging procedures; the circle of ideas concerning the Radon transform, going back to the seminal work of Funck and Radon around 1916–1917; and integralgeometric transforms which are now being used in the study of field equations in mathematical physics. Some of these areas also involve grouprepresentation theoretic problems.

Table of Contents

Articles

Carlos A. Berenstein — Spectral synthesis on symmetric spaces [ MR 876311 ]

Ethan D. Bolker — The finite Radon transform [ MR 876312 ]

Edward G. Dunne — Hyperfunctions in representation theory and mathematical physics [ MR 876313 ]

David V. Finch and Alexander Hertle — The exponential Radon transform [ MR 876314 ]

S. G. Gindikin — Integral geometry as geometry and as analysis [ MR 876315 ]

Eric L. Grinberg — Euclidean Radon transforms: ranges and restrictions [ MR 876316 ]

Victor Guillemin — Perspectives in integral geometry [ MR 876317 ]

S. Helgason — Some results on Radon transforms, Huygens’ principle and Xray transforms [ MR 876318 ]

Ralph Howard — Classical integral geometry in Riemannian homogeneous spaces [ MR 876319 ]

Kenneth D. Johnson — Differential operators and Cartan motion groups [ MR 876320 ]

Lisa A. Mantini — An $L^2$cohomology analogue of the Penrose transform for the oscillator representation [ MR 876321 ]

Eric Todd Quinto — Injectivity of rotation invariant Radon transforms on complex hyperplanes in ${\bf C}^n$ [ MR 876322 ]

Radu Roşu — On overdetermined systems associated with integral geometry transforms in the real projective space [ MR 876323 ]

M. Shahshahani and Alladi Sitaram — The Pompeiu problem in exterior domains in symmetric spaces [ MR 876324 ]

Theodore Shifrin — Curvature integrals and Chern classes of singular varieties [ MR 876325 ]

Peter Waksman — Hypothesis testing in integral geometry: guessing the shape of a plane domain [ MR 876326 ]

R. S. Ward — Nonlinear integral transforms [ MR 876327 ]

R. O. Wells, Jr. — Integral geometry and twistor theory [ MR 876328 ]

Lawrence Zalcman — Some inverse problems of potential theory [ MR 876329 ]


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The topic of integral geometry is not as well known as its counterpart, differential geometry. However, research in integral geometry has indicated that this field may yield as equally deep insights as differential geometry has into the global and local nature of manifolds and the functions on them. In 1984, an AMSIMSSIAM joint summer research conference on integral geometry was held at Bowdoin College. This volume consists of papers presented there.
The papers range from purely expository to quite technical and represent a good survey of contemporary work in integral geometry. Three major areas are covered: the classical problems of computing geometric invariants by statistical averaging procedures; the circle of ideas concerning the Radon transform, going back to the seminal work of Funck and Radon around 1916–1917; and integralgeometric transforms which are now being used in the study of field equations in mathematical physics. Some of these areas also involve grouprepresentation theoretic problems.

Articles

Carlos A. Berenstein — Spectral synthesis on symmetric spaces [ MR 876311 ]

Ethan D. Bolker — The finite Radon transform [ MR 876312 ]

Edward G. Dunne — Hyperfunctions in representation theory and mathematical physics [ MR 876313 ]

David V. Finch and Alexander Hertle — The exponential Radon transform [ MR 876314 ]

S. G. Gindikin — Integral geometry as geometry and as analysis [ MR 876315 ]

Eric L. Grinberg — Euclidean Radon transforms: ranges and restrictions [ MR 876316 ]

Victor Guillemin — Perspectives in integral geometry [ MR 876317 ]

S. Helgason — Some results on Radon transforms, Huygens’ principle and Xray transforms [ MR 876318 ]

Ralph Howard — Classical integral geometry in Riemannian homogeneous spaces [ MR 876319 ]

Kenneth D. Johnson — Differential operators and Cartan motion groups [ MR 876320 ]

Lisa A. Mantini — An $L^2$cohomology analogue of the Penrose transform for the oscillator representation [ MR 876321 ]

Eric Todd Quinto — Injectivity of rotation invariant Radon transforms on complex hyperplanes in ${\bf C}^n$ [ MR 876322 ]

Radu Roşu — On overdetermined systems associated with integral geometry transforms in the real projective space [ MR 876323 ]

M. Shahshahani and Alladi Sitaram — The Pompeiu problem in exterior domains in symmetric spaces [ MR 876324 ]

Theodore Shifrin — Curvature integrals and Chern classes of singular varieties [ MR 876325 ]

Peter Waksman — Hypothesis testing in integral geometry: guessing the shape of a plane domain [ MR 876326 ]

R. S. Ward — Nonlinear integral transforms [ MR 876327 ]

R. O. Wells, Jr. — Integral geometry and twistor theory [ MR 876328 ]

Lawrence Zalcman — Some inverse problems of potential theory [ MR 876329 ]