Orthogonal Polynomials of Several Variables / Edition 1

Orthogonal Polynomials of Several Variables / Edition 1

by Charles F. Dunkl, Yuan Xu
     
 

ISBN-10: 0521800439

ISBN-13: 9780521800433

Pub. Date: 03/28/2001

Publisher: Cambridge University Press

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

Overview

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.

Product Details

ISBN-13:
9780521800433
Publisher:
Cambridge University Press
Publication date:
03/28/2001
Series:
Encyclopedia of Mathematics and its Applications Series, #81
Edition description:
New Edition
Pages:
408
Product dimensions:
6.14(w) x 9.21(h) x 0.94(d)

Table of Contents

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.

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