Orthogonal Polynomials of Several Variables
2nd Edition
Published on 21. August 2014
Book
Hardback
426 pages
978-1-107-07189-6 (ISBN)
Description
Serving both as an introduction to the subject and as a reference, this book presents the theory in elegant form and with modern concepts and notation. It covers the general theory and emphasizes the classical types of orthogonal polynomials whose weight functions are supported on standard domains. The approach is a blend of classical analysis and symmetry group theoretic methods. Finite reflection groups are used to motivate and classify symmetries of weight functions and the associated polynomials. This revised edition has been updated throughout to reflect recent developments in the field. It contains 25% new material, including two brand new chapters on orthogonal polynomials in two variables, which will be especially useful for applications, and orthogonal polynomials on the unit sphere. The most modern and complete treatment of the subject available, it will be useful to a wide audience of mathematicians and applied scientists, including physicists, chemists and engineers.
Reviews / Votes
Review of the first edition: 'This book is the first modern treatment of orthogonal polynomials of several real variables. It presents not only a general theory, but also detailed results of recent research on generalizations of various classical cases.' Mathematical Reviews Review of the first edition: 'This book is very impressive and shows the richness of the theory.' Vilmos Totik, Acta Scientiarum Mathematicarum 'This is a valuable book for anyone with an interest in special functions of several variables.' Marcel de Jeu, American Mathematical SocietyMore details
Series
Edition
2nd Revised edition
Language
English
Place of publication
Cambridge
United Kingdom
Target group
Professional and scholarly
Edition type
Revised edition
Illustrations
1 Halftones, unspecified; 2 Line drawings, unspecified
Dimensions
Height: 240 mm
Width: 161 mm
Thickness: 30 mm
Weight
903 gr
ISBN-13
978-1-107-07189-6 (9781107071896)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Charles F. Dunkl
Orthogonal Polynomials of Several Variables
E-Book
08/2014
Cambridge University Press
€108.99
Available for download
Charles F. Dunkl | Yuan Xu
Orthogonal Polynomials of Several Variables
E-Book
08/2014
2nd Edition
Cambridge University Press
€98.99
Available for download
Previous edition
Charles F. Dunkl | Yuan Xu
Orthogonal Polynomials of Several Variables
Book
02/2001
Cambridge University Press
€154.74
Article exhausted; check for reprint
Persons
Charles F. Dunkl is Professor Emeritus of Mathematics at the University of Virginia. Among his work one finds the seminal papers containing the construction of differential-difference operators associated to finite reflection groups and related integral transforms. Aspects of the theory are now called Dunkl operators, the Dunkl transform, and the Dunkl kernel. Dunkl is a Fellow of the Institute of Physics, and a member of SIAM and of its Activity Group on Orthogonal Polynomials and Special Functions, which he founded in 1990 and then chaired from 1990 to 1998. Yuan Xu is Professor of Mathematics at the University of Oregon. His work covers topics in approximation theory, harmonic analysis, numerical analysis, orthogonal polynomials and special functions, and he works mostly in problems of several variables. Xu is currently on the editorial board of five international journals and has been a plenary or invited speaker in numerous international conferences. He was awarded a Humboldt research fellowship in 1992-93 and received a Faculty Excellence Award at the University of Oregon in 2009. He is a member of SIAM and of its Activity Group on Orthogonal Polynomials and Special Functions.
Content
Preface to the second edition; Preface to the first edition; 1. Background; 2. Orthogonal polynomials in two variables; 3. General properties of orthogonal polynomials in several variables; 4. Orthogonal polynomials on the unit sphere; 5. Examples of orthogonal polynomials in several variables; 6. Root systems and Coxeter groups; 7. Spherical harmonics associated with reflection groups; 8. Generalized classical orthogonal polynomials; 9. Summability of orthogonal expansions; 10. Orthogonal polynomials associated with symmetric groups; 11. Orthogonal polynomials associated with octahedral groups and applications; References; Author index; Symbol index; Subject index.