Hypergeometric Functions On Domains Of Positivity Jack Polynomials And Applications

Author : Donald St. P. Richards
Publisher : American Mathematical Soc.
Page : 259 pages
File Size : 40,6 Mb
Release : 1992
Category : Mathematics
ISBN : 9780821851593

Get Book

Hypergeometric Functions on Domains of Positivity, Jack Polynomials, and Applications by Donald St. P. Richards Pdf

This book is the first set of proceedings to be devoted entirely to the theory of hypergeometric functions defined on domains of positivity. Most of the scientific areas in which these functions are applied include analytic number theory, combinatorics, harmonic analysis, random walks, representation theory, and mathematical physics--are represented here. This volume is based largely on lectures presented at a Special Session at the AMS meeting in Tampa, Florida in March 1991, which was devoted to hypergeometric functions of matrix argument and to fostering communication among representatives of the diverse scientific areas in which these functions are utilized. Accessible to graduate students and others seeking an introduction to the state of the art in this area, this book is a suitable text for advanced graduate seminar courses for it contains many open problems.

Author : Vadim B. Kuznetsov,Hall-Littlewood Workshop on Jack
Publisher : American Mathematical Soc.
Page : 386 pages
File Size : 48,8 Mb
Release : 2006
Category : Orthogonal polynomials
ISBN : 9780821836835

Get Book

Jack, Hall-Littlewood and Macdonald Polynomials by Vadim B. Kuznetsov,Hall-Littlewood Workshop on Jack Pdf

The subject of symmetric functions began with the work of Jacobi, Schur, Weyl, Young and others on the Schur polynomials. In the 1950's and 60's, far-reaching generalizations of Schur polynomials were obtained by Hall and Littlewood (independently) and, in a different direction, by Jack. In the 1980's, Macdonald unified these developments by introducing a family of polynomials associated with arbitrary root systems. The last twenty years have witnessed considerable progress in this area, revealing new and profound connections with representation theory, algebraic geometry, combinatorics, special functions, classical analysis and mathematical physics. All these fields and more are represented in this volume, which contains the proceedings of a conference on ``Jack, Hall-Littlewood and Macdonald polynomials'' held at ICMS, Edinburgh, during September 23-26, 2003. In addition to new results by leading researchers, the book contains a wealth of historical material, including brief biographies of Hall, Littlewood, Jack and Macdonald; the original papers of Littlewood and Jack; notes on Hall's work by Macdonald; and a recently discovered unpublished manuscript by Jack (annotated by Macdonald). The book will be invaluable to students and researchers who wish to learn about this beautiful and exciting subject.

Author : Bhatia Rajendra,Pal Arup,Rangarajan G
Publisher : World Scientific
Page : 4144 pages
File Size : 45,6 Mb
Release : 2011-06-06
Category : Mathematics
ISBN : 9789814462938

Get Book

Proceedings Of The International Congress Of Mathematicians 2010 (Icm 2010) (In 4 Volumes) - Vol. I: Plenary Lectures And Ceremonies, Vols. Ii-iv: Invited Lectures by Bhatia Rajendra,Pal Arup,Rangarajan G Pdf

ICM 2010 proceedings comprises a four-volume set containing articles based on plenary lectures and invited section lectures, the Abel and Noether lectures, as well as contributions based on lectures delivered by the recipients of the Fields Medal, the Nevanlinna, and Chern Prizes. The first volume will also contain the speeches at the opening and closing ceremonies and other highlights of the Congress.

Author : SPRINGER
Publisher : Springer Science & Business Media
Page : 259 pages
File Size : 40,6 Mb
Release : 2024-07-01
Category : Electronic
ISBN : 9783540403753

Get Book

Orthogonal Polynomials and Special Functions by SPRINGER Pdf

Author : Stephen Rallis
Publisher : Walter de Gruyter
Page : 442 pages
File Size : 42,7 Mb
Release : 2005
Category : Mathematics
ISBN : 3110179393

Get Book

Automorphic Representations, L-functions and Applications by Stephen Rallis Pdf

This volume is the proceedings of the conference on Automorphic Representations, L-functions and Applications: Progress and Prospects, held at the Department of Mathematics of The Ohio State University, March 27-30, 2003, in honor of the 60th birthday of Steve Rallis. The theory of automorphic representations, automorphic L-functions and their applications to arithmetic continues to be an area of vigorous and fruitful research. The contributed papers in this volume represent many of the most recent developments and directions, including Rankin-Selberg L-functions (Bump, Ginzburg-Jiang-Rallis, Lapid-Rallis) the relative trace formula (Jacquet, Mao-Rallis) automorphic representations (Gan-Gurevich, Ginzburg-Rallis-Soudry) representation theory of p-adic groups (Baruch, Kudla-Rallis, Moeglin, Cogdell-Piatetski-Shapiro-Shahidi) p-adic methods (Harris-Li-Skinner, Vigneras), and arithmetic applications (Chinta-Friedberg-Hoffstein). The survey articles by Bump, on the Rankin-Selberg method, and by Jacquet, on the relative trace formula, should be particularly useful as an introduction to the key ideas about these important topics. This volume should be of interest both to researchers and students in the area of automorphic representations, as well as to mathematicians in other areas interested in having an overview of current developments in this important field.

Author : P.K. Suetin
Publisher : Routledge
Page : 368 pages
File Size : 51,6 Mb
Release : 2022-04-01
Category : Mathematics
ISBN : 9781351426381

Get Book

Orthogonal Polynomials in Two Variables by P.K. Suetin Pdf

Presenting a comprehensive theory of orthogonal polynomials in two real variables and properties of Fourier series in these polynomials, this volume also gives cases of orthogonality over a region and on a contour. The text includes the classification of differential equations which admits orthogonal polynomials as eigenfunctions and several two-dimensional analogies of classical orthogonal polynomials.

Author : David E. Keyes,Jinchao Xu
Publisher : American Mathematical Soc.
Page : 546 pages
File Size : 43,7 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821851715

Get Book

Domain Decomposition Methods in Scientific and Engineering Computing by David E. Keyes,Jinchao Xu Pdf

This book contains proceedings from the Seventh International Conference on Domain Decomposition Methods, held at Pennsylvania State University in October 1993. The term ``domain decomposition'' has for nearly a decade been associated with the partly iterative, partly direct algorithms explored in the proceedings of this conference. Noteworthy trends in the current volume include progress in dealing with so-called ``bad parameters'' in elliptic partial differential equation problems, as well as developments in partial differential equations outside of the elliptically-dominated framework. Also described here are convergence and complexity results for novel discretizations, which bring with them new challenges in the derivation of appropriate operators for coarsened spaces. Implementations and architectural considerations are discussed, as well as partitioning tools and environments. In addition, the book describes a wide array of applications, from semiconductor device simulation to structural mechanics to aerodynamics. Presenting many of the latest results in the field, this book offers readers an up-to-date guide to the many facets of the theory and practice of domain decomposition.

Author : Charles F. Dunkl,Yuan Xu
Publisher : Cambridge University Press
Page : 408 pages
File Size : 51,8 Mb
Release : 2001-02-22
Category : Mathematics
ISBN : 9780521800433

Get Book

Orthogonal Polynomials of Several Variables by Charles F. Dunkl,Yuan Xu Pdf

Orthogonal polynomials of several variables, approximation theory, symmetry-group methods.

Author : Guo Chun Wen
Publisher : World Scientific
Page : 436 pages
File Size : 48,6 Mb
Release : 2011
Category : Mathematics
ISBN : 9789814327862

Get Book

Boundary Value Problems, Integral Equations and Related Problems by Guo Chun Wen Pdf

In this volume, we report new results about various boundary value problems for partial differential equations and functional equations, theory and methods of integral equations and integral operators including singular integral equations, applications of boundary value problems and integral equations to mechanics and physics, numerical methods of integral equations and boundary value problems, theory and methods for inverse problems of mathematical physics, Clifford analysis and related problems. Contributors include: L Baratchart, B L Chen, D C Chen, S S Ding, K Q Lan, A Farajzadeh, M G Fei, T Kosztolowicz, A Makin, T Qian, J M Rassias, J Ryan, C-Q Ru, P Schiavone, P Wang, Q S Zhang, X Y Zhang, S Y Du, H Y Gao, X Li, Y Y Qiao, G C Wen, Z T Zhang, and others.

Author : Alfio Quarteroni
Publisher : American Mathematical Soc.
Page : 484 pages
File Size : 46,6 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821851586

Get Book

Domain Decomposition Methods in Science and Engineering by Alfio Quarteroni Pdf

This book contains the proceedings of the Sixth International Conference on Domain Decomposition, held in June 1992 in Como, Italy. Developments in this area are driven by advances in computer technology as well as by a strengthening in the mathematical foundations of the subject. Compared to just a few years ago, experts have much more experience with difficult applications and have accumulated solid evidence that these methods provide valuable tools for solving problems in science and engineering. Much of the work in this field focuses on developing numerical methods for large algebraic systems, methods central to producing efficient codes for computational fluid dynamics, elasticity, and other core problems of continuum mechanics. These methods hold the promise of allowing simulations of very high resolution with relative ease. This approach allows for the flexibility of using different numerical methods and different models, each appropriate for the subregion at hand, to solve large problems in a cost-effective way. Containing contributions by international experts in this area, this book reports on the state-of-the-art in the growing field of domain decomposition.

Author : Eric M. Rains,S. Ole Warnaar
Publisher : American Mathematical Soc.
Page : 115 pages
File Size : 40,7 Mb
Release : 2021-07-21
Category : Education
ISBN : 9781470446901

Get Book

Bounded Littlewood Identities by Eric M. Rains,S. Ole Warnaar Pdf

We describe a method, based on the theory of Macdonald–Koornwinder polynomials, for proving bounded Littlewood identities. Our approach provides an alternative to Macdonald’s partial fraction technique and results in the first examples of bounded Littlewood identities for Macdonald polynomials. These identities, which take the form of decomposition formulas for Macdonald polynomials of type (R, S) in terms of ordinary Macdonald polynomials, are q, t-analogues of known branching formulas for characters of the symplectic, orthogonal and special orthogonal groups. In the classical limit, our method implies that MacMahon’s famous ex-conjecture for the generating function of symmetric plane partitions in a box follows from the identification of GL(n, R), O(n) as a Gelfand pair. As further applications, we obtain combinatorial formulas for characters of affine Lie algebras; Rogers–Ramanujan identities for affine Lie algebras, complementing recent results of Griffin et al.; and quadratic transformation formulas for Kaneko–Macdonald-type basic hypergeometric series.

Author : Stephen Berman
Publisher : American Mathematical Soc.
Page : 154 pages
File Size : 40,6 Mb
Release : 2005
Category : Mathematics
ISBN : 9780821837016

Get Book

Infinite-dimensional Aspects of Representation Theory and Applications by Stephen Berman Pdf

The University of Virginia (Charlottesville) hosted an international conference on Infinite-dimensional Aspects of Representation Theory and Applications. This volume contains papers resulting from the mini-courses and talks given at the meeting. Beyond the techniques and ideas related to representation theory, the book demonstrates connections to number theory, algebraic geometry, and mathematical physics. The specific topics covered include Hecke algebras, quantum groups, infinite-dimensional Lie algebras, quivers, modular representations, and Gromov-Witten invariants. The book is suitable for graduate students and researchers interested in representation theory.

Author : Niky Kamran,Peter J. Olver
Publisher : American Mathematical Soc.
Page : 310 pages
File Size : 47,9 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821851692

Get Book

Lie Algebras, Cohomology, and New Applications to Quantum Mechanics, by Niky Kamran,Peter J. Olver Pdf

This volume is devoted to a range of important new ideas arising in the applications of Lie groups and Lie algebras to Schrodinger operators and associated quantum mechanical systems. In these applications, the group does not appear as a standard symmetry group, but rather as a "hidden" symmetry group whose representation theory can still be employed to analyze at least part of the spectrum of the operator. In light of the rapid developments in this subject, a Special Session was organized at the AMS meeting at Southwest Missouri State University in March 1992 in order to bring together, perhaps for the first time, mathematicians and physicists working in closely related areas. The contributions to this volume cover Lie group methods, Lie algebras and Lie algebra cohomology, representation theory, orthogonal polynomials, q-series, conformal field theory, quantum groups, scattering theory, classical invariant theory, and other topics. This volume, which contains a good balance of research and survey papers, presents at look at some of the current development in this extraordinarily rich and vibrant area.

Author : William Abikoff,Joan S. Birman,Kathryn Kuiken
Publisher : American Mathematical Soc.
Page : 499 pages
File Size : 46,5 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821851562

Get Book

The Mathematical Legacy of Wilhelm Magnus by William Abikoff,Joan S. Birman,Kathryn Kuiken Pdf

Wilhelm Magnus was an extraordinarily creative mathematician who made fundamental contributions to diverse areas, including group theory, geometry, and special functions. This book contains the proceedings of a conference held in May 1992 at Polytechnic University to honor the memory of Magnus. The focus of the book is on active areas of current research where Magnus' influence can be seen. The papers range from expository articles to major new research, bringing together seemingly diverse topics and providing entry points to a variety of areas of mathematics.

Author : Alejandro Adem,R. James Milgram,Douglas C. Ravenel
Publisher : American Mathematical Soc.
Page : 250 pages
File Size : 48,7 Mb
Release : 1995
Category : Homotopy theory
ISBN : 9780821803059

Get Book

Homotopy Theory and Its Applications by Alejandro Adem,R. James Milgram,Douglas C. Ravenel Pdf

This book is the result of a conference held to examine developments in homotopy theory in honor of Samuel Gitler in July 1993 (Cocoyoc, Mexico). It includes several research papers and three expository papers on various topics in homotopy theory. The research papers discuss the following: BL application of homotopy theory to group theory BL fiber bundle theory BL homotopy theory The expository papers consider the following topics: BL the Atiyah-Jones conjecture (by C. Boyer) BL classifying spaces of finite groups (by J. Martino) BL instanton moduli spaces (by J. Milgram) Homotopy Theory and Its Applications offers a distinctive account of how homotopy theoretic methods can be applied to a variety of interesting problems.