Edited by: Robert S. Doran, Texas Christian University, Fort Worth, TX,
and V. S. Varadarajan, University of California, Los Angeles, CA
The Mathematical Legacy of Harish-Chandra:
A Celebration of Representation Theory and Harmonic Analysis
Description
Harish-Chandra was a mathematician of great power, vision, and remarkable ingenuity. His profound contributions to the representation theory of Lie groups, harmonic analysis, and related areas left researchers a rich legacy that continues today. This book presents the proceedings of an AMS Special Session entitled, "Representation Theory and Noncommutative Harmonic Analysis: A Special Session Honoring the Memory of Harish-Chandra", which marked 75 years since his birth and 15 years since his untimely death at age 60.
Contributions to the volume were written by an outstanding group of internationally known mathematicians. Included are expository and historical surveys and original research papers. The book also includes talks given at the IAS Memorial Service in 1983 by colleagues who knew Harish-Chandra well. Also reprinted are two articles entitled, "Some Recollections of Harish-Chandra", by A. Borel, and "Harish-Chandra's c-Function: A Mathematical Jewel", by S. Helgason. In addition, an expository paper, "An Elementary Introduction to Harish-Chandra's Work", gives an overview of some of his most basic mathematical ideas with references for further study.
This volume offers a comprehensive retrospective of Harish-Chandra's professional life and work. Personal recollections give the book particular significance. Readers should have an advanced-level background in the representation theory of Lie groups and harmonic analysis.
Contents
V. S. Varadarajan -- Harish-Chandra, his work, and its legacy
A. Borel -- Some recollections of Harish-Chandra
S. Helgason -- Harish-Chandra memorial talk
R. P. Langlands -- Harish-Chandra memorial talk
G. D. Mostow -- Harish-Chandra memorial talk
V. S. Varadarajan -- Harish-Chandra memorial talk
R. A. Herb -- An elementary introduction to Harish-Chandra's work
J. Arthur -- Stabilization of a family of differential equations
D. Barbasch -- Orbital integrals of nilpotent orbits
P. F. Baum, N. Higson, and R. J. Plymen -- Representation theory of p-adic groups: A view from operator algebras
W. Casselman, H. Hecht, and D. Milicic -- Bruhat filtrations and Whittaker vectors for real groups
S. DeBacker and P. J. Sally, Jr. -- Germs, characters, and the Fourier transforms of nilpotent orbits
H. Ding, K. I. Gross, R. A. Kunze, and D. St. P. Richards -- Bessel functions on boundary orbits and singular holomorphic representations
B. Gross and N. Wallach -- Restriction of small discrete series representations to symmetric subgroups
S. Helgason -- Harish-Chandra's c-function. A mathematical jewel
R. A. Herb -- Two-structures and discrete series character formulas
R. E. Howe -- Harish-Chandra homomorphisms
P. E. T. Jorgensen and G. ?lafsson -- Unitary representations and Osterwalder-Schrader duality
A. W. Knapp -- Intertwining operators and small unitary representations
R. A. Kunze -- On some problems in analysis suggested by representation theory
R. L. Lipsman -- Distributional reciprocity and generalized Gelfand pairs
A. Moy -- Displacement functions on the Bruhat-Tits building
F. Murnaghan -- Germs of characters of admissible representations
B. Speh -- Seiberg-Witten equations on locally symmetric spaces
J. A. Wolf and R. Zierau -- Holomorphic double fibration transforms
Details:
Publisher: American Mathematical Society
Series: Proceedings of Symposia in Pure Mathematics, Volume: 68
Publication Year: 2000
ISBN: 0-8218-1197-5
Paging: 549 pp.
Binding: Hardcover
Jun-ichi Igusa, Johns Hopkins University, Baltimore, MD
An Introduction to the Theory of Local Zeta Functions
Description
This book is an introductory presentation to the theory of local zeta functions. As distributions, and mostly in the archimedian case, local zeta functions are called complex powers.
The volume contains major results on complex powers by Atiyah, Bernstein, I. M. Gelfand, and S. I. Gelfand. Also included are related results by Sato. The section on p-adic local zeta functions presents Serre's structure theorem, a rationality theorem and many examples by the author. It concludes with theorems by Denef and Meuser.
Prerequisites for understanding the text include basic courses in algebra, calculus, complex analysis, and general topology. The book follows the usual pattern of progress in mathematics: examples are given, conjectures follow, conjectures are developed into theorems.
This book is accessible and self-contained. Results illustrate the unity of mathematics by gathering important theorems from algebraic geometry and singularity theory, number theory, algebra, topology, and analysis. The ideas are then employed in essential ways to prove the theorems.
Titles in this series are co-published with International Press, Cambridge, MA.
Contents
Preliminaries
Implicit function theorems and K-analytic manifolds
Hironaka's desingularization theorem
Bernstein's theory
Archimedean local zeta functions
Prehomogeneous vector spaces
Totally disconnected spaces and p-adic manifolds
Local zeta functions (p-adic case)
Some homogeneous polynomials
Computation of Z(s)
Theorems of Denef and Meuser
Bibliography
Index
Details:
Publisher: American Mathematical Society, International Press
Series: AMS/IP Studies in Advanced Mathematics, Volume: 14
Publication Year: 2000
ISBN: 0-8218-2015-X
Paging: 232 pp.
Edited by: K. Boroczky, Jr., Hungarian Academy of Sciences, Budapest, Hungary,
W. Neumann, University of Melbourne, Parkville, Australia,
and A. Stipsicz, Eotvos Lorend University, Budapest, Hungary
Low Dimensional Topology
A publication of Jonos Bolyai Mathematical Society.
Description
This proceedings volume contains the notes of five lectures given at the Summer School on Low Dimensional Topology held at the Hungarian Institute of Sciences (Budapest). Topics discussed and presented in this book are "Differential Topology of 4-dimensional Manifolds" by J. Morgan, "The Link of Surface Singularities" by A.
N?methi, "Nonpositively Curved Spaces" by M. Davis, "Geometry of 3-manifolds" by W. D. Neumann, and "Some Topological Invariants of Isolated Hypersurface Singularities" by A. Nemethi. Each lecture was accompanied by tutorials presenting important examples for the presented theory.
The articles in this book offer a comprehensive and up-to-date introduction to each field.
Contents
Introduction
M. Davis and G. Moussong -- Notes on nonpositively curved polyhedra
J. W. Morgan -- Smooth invariants of 4-manifolds
W. D. Neumann -- Notes on geometry and 3-manifolds
A. Nomethi -- Normal surface singularities
A. Nomethi -- Some topological invariants of isolated hypersurface singularities
Details:
Publisher: Jonos Bolyai Mathematical Society
Distributor: American Mathematical Society
Series: Bolyai Society Mathematical Studies, Volume: 8
Publication Year: 1999
ISBN: 963-8022-92-2
Paging: 413 pp.
Binding: Hardcover
Patrice Le Calvez, University of Paris, Villetaneuse, France
Dynamical Properties of Diffeomorphisms of the Annulus and of the Torus
Description
The first chapter of this monograph presents a survey of the theory of monotone twist maps of the annulus. First, the author covers the conservative case by presenting a short survey of Aubry-Mather theory and Birkhoff theory, followed by some criteria for existence of periodic orbits without the area-preservation property. These are applied in the area-decreasing case, and the properties of Birkhoff attractors are discussed. A diffeomorphism of the closed annulus which is isotopic to the identity can be written as the composition of monotone twist maps.
The second chapter generalizes some aspects of Aubry-Mather theory to such maps and presents a version of the Poincar?-Birkhoff theorem in which the periodic orbits have the same braid type as in the linear case. A diffeomorphism of the torus isotopic to the identity is also a composition of twist maps, and it is possible to obtain a proof of the Conley-Zehnder theorem with the same kind of conclusions about the braid type, in the case of periodic orbits. This result leads to an equivariant version of the Brouwer translation theorem which permits new proofs of some results about the rotation set of diffeomorphisms of the torus.
This is the English translation of a volume previously published as volume 204 in the Asterisque series.
Contents
Presentation and comparison of the different approaches to the theory of montone twist diffeomorphisms of the annulus
Generating phases of the diffeomorphisms of the torus and the annulus
Bibliography
Index
Details:
Publisher: American Mathematical Society
Series: SMF/AMS Texts and Monographs, Volume: 4
Publication Year: 2000
ISBN: 0-8218-1943-7
Paging: 105 pp.
Binding: Softcover
V. V. Buldygin, Kyev Politechnic Institute, Ukraine,
and Yu. V. Kozachenko, Kyev Taras Shevchenko National University, Ukraine
Metric Characterization of Random Variables and Random Processes
Description
The topic covered in this book is the study of metric and other close characteristics of different spaces and classes of random variables and the application of the entropy method to the investigation of properties of stochastic processes whose values, or increments, belong to given spaces. The following processes appear in detail: pre-Gaussian processes, shot noise processes representable as integrals over processes with independent increments, quadratically Gaussian processes, and, in particular, correlogram-type estimates of the correlation function of a stationary Gaussian process, jointly strictly sub-Gaussian processes, etc.
The book consists of eight chapters divided into four parts: The first part deals with classes of random variables and their metric characteristics. The second part presents properties of stochastic processes "imbedded" into a space of random variables discussed in the first part. The third part considers applications of the general theory. The fourth part outlines the necessary auxiliary material.
Problems and solutions presented show the intrinsic relation existing between probability methods, analytic methods, and functional methods in the theory of stochastic processes. The concluding sections, "Comments" and "References", gives references to the literature used by the authors in writing the book.
Contents
Sub-Gaussian and pre-Gaussian random variables
Orlicz spaces of random variables
Regularity of sample paths of a stochastic process
Pre-Gaussian processes
Shot noise processes and their properties
Correlograms of stationary Gaussian processes
Jointly sub-Gaussian, super-Gaussian, and pseudo-Gaussian stochastic processes
Appendices
Comments
References
Basic notation
Index
Details:
Publisher: American Mathematical Society
Series: Translations of Mathematical Monographs, Volume: 188
Publication Year: 2000
ISBN: 0-8218-0533-9
Paging: approximately 264 pp.
Binding: Hardcover