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Hardcover ISBN:  9780821834725 
Product Code:  TRANS2/210 
List Price:  $175.00 
MAA Member Price:  $157.50 
AMS Member Price:  $140.00 
eBook ISBN:  9781470434212 
Product Code:  TRANS2/210.E 
List Price:  $165.00 
MAA Member Price:  $148.50 
AMS Member Price:  $132.00 
Hardcover ISBN:  9780821834725 
eBook ISBN:  9781470434212 
Product Code:  TRANS2/210.B 
List Price:  $340.00 $257.50 
MAA Member Price:  $306.00 $231.75 
AMS Member Price:  $272.00 $206.00 

Book DetailsAmerican Mathematical Society Translations  Series 2Advances in the Mathematical SciencesVolume: 210; 2003; 355 ppMSC: Primary 22; 53; 00
The book contains survey and research articles devoted mainly to geometry and harmonic analysis of symmetric spaces and to corresponding aspects of group representation theory. The volume is dedicated to the memory of Russian mathematician, F. I. Karpelevich (1927–2000).
Of particular interest are the survey articles by Sawyer on the Abel transform on noncompact Riemannian symmetric spaces, and by Anker and Ostellari on estimates for heat kernels on such spaces, as well as the article by Bernstein and Gindikin on integral geometry for families of curves. There are also many research papers on topics of current interest.
The book is suitable for graduate students and research mathematicians interested in harmonic analysis and representation theory.
ReadershipGraduate students and research mathematicians interested in harmonic analysis and representation theory.

Table of Contents

Chapters

Dmitri N. Akhiezer — Asymptotic distribution of eigenvalues for certain elements of the group ring of a compact Lie group

Dmitri V. Alekseevsky and Antonio J. Di Scala — Minimal homogeneous submanifolds of symmetric spaces

JeanPhilippe Anker and Patrick Ostellari — The heat kernel on noncompact symmetric spaces

Ehud Moshe Baruch, Ilya PiatetskiShapiro and Stephen Rallis — On the uniqueness of Fourier Jacobi models for representations of $U(2,1)$

Joseph Bernstein and Simon Gindikin — Notes on integral geometry for manifolds of curves

Benjamin Enriquez and Pavel Etingof — Quantization of AlekseevMeinrenken dynamical $r$matrices

Jacques Faraut — Analysis on the crown of a Riemannian symmetric space

Israel Gelfand, Vladimir Retakh and Robert Lee Wilson — Quaternionic quasideterminants and determinants

Simon Gindikin — Product formula for $c$function and inverse horospherical transform

J. Hilgert, A. Pasquale and E. B. Vinberg — The dual horospherical Radon transform as a limit of spherical Radon transforms

A. W. Knapp — The GindikinKarpelevič formula and intertwining operators

Toshiyuki Kobayashi and Salma Nasrin — Multiplicity one theorem in the orbit method

Bernhard Krötz and Gestur Ólafsson — The cfunction for noncompactly causal symmetric spaces and its relations to harmonic analysis and representation theory

I. G. Macdonald — A formal identity for affine root systems

V. F. Molchanov — Canonical representations and overgroups

Yurii A. Neretin — Pencils of geodesics in symmetric spaces, Karpelevich boundary, and associahedronlike polyhedra

M. A. Olshanetsky and V.B. K. Rogov — Poisson formula for a family of noncommutative Lobachevsky spaces

A. L. Onishchik — Real semisimple Lie algebras and their representations

Toshio Oshima — A calculation of $c$functions for semisimple symmetric spaces

P. Sawyer — The Abel transform on symmetric spaces of noncompact type


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The book contains survey and research articles devoted mainly to geometry and harmonic analysis of symmetric spaces and to corresponding aspects of group representation theory. The volume is dedicated to the memory of Russian mathematician, F. I. Karpelevich (1927–2000).
Of particular interest are the survey articles by Sawyer on the Abel transform on noncompact Riemannian symmetric spaces, and by Anker and Ostellari on estimates for heat kernels on such spaces, as well as the article by Bernstein and Gindikin on integral geometry for families of curves. There are also many research papers on topics of current interest.
The book is suitable for graduate students and research mathematicians interested in harmonic analysis and representation theory.
Graduate students and research mathematicians interested in harmonic analysis and representation theory.

Chapters

Dmitri N. Akhiezer — Asymptotic distribution of eigenvalues for certain elements of the group ring of a compact Lie group

Dmitri V. Alekseevsky and Antonio J. Di Scala — Minimal homogeneous submanifolds of symmetric spaces

JeanPhilippe Anker and Patrick Ostellari — The heat kernel on noncompact symmetric spaces

Ehud Moshe Baruch, Ilya PiatetskiShapiro and Stephen Rallis — On the uniqueness of Fourier Jacobi models for representations of $U(2,1)$

Joseph Bernstein and Simon Gindikin — Notes on integral geometry for manifolds of curves

Benjamin Enriquez and Pavel Etingof — Quantization of AlekseevMeinrenken dynamical $r$matrices

Jacques Faraut — Analysis on the crown of a Riemannian symmetric space

Israel Gelfand, Vladimir Retakh and Robert Lee Wilson — Quaternionic quasideterminants and determinants

Simon Gindikin — Product formula for $c$function and inverse horospherical transform

J. Hilgert, A. Pasquale and E. B. Vinberg — The dual horospherical Radon transform as a limit of spherical Radon transforms

A. W. Knapp — The GindikinKarpelevič formula and intertwining operators

Toshiyuki Kobayashi and Salma Nasrin — Multiplicity one theorem in the orbit method

Bernhard Krötz and Gestur Ólafsson — The cfunction for noncompactly causal symmetric spaces and its relations to harmonic analysis and representation theory

I. G. Macdonald — A formal identity for affine root systems

V. F. Molchanov — Canonical representations and overgroups

Yurii A. Neretin — Pencils of geodesics in symmetric spaces, Karpelevich boundary, and associahedronlike polyhedra

M. A. Olshanetsky and V.B. K. Rogov — Poisson formula for a family of noncommutative Lobachevsky spaces

A. L. Onishchik — Real semisimple Lie algebras and their representations

Toshio Oshima — A calculation of $c$functions for semisimple symmetric spaces

P. Sawyer — The Abel transform on symmetric spaces of noncompact type