Orthogonal Polynomials of Several Variables

Updated throughout, this revised edition contains 25% new material covering progress made in the field over the past decade.

Charles F. Dunkl (Author), Yuan Xu (Author)

9781107071896, Cambridge University Press

Hardback, published 21 August 2014

426 pages, 3 b/w illus.
24 x 15.9 x 2.8 cm, 0.81 kg

'This is a valuable book for anyone with an interest in special functions of several variables.' Marcel de Jeu, American Mathematical Society

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.

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.

Subject Areas: Complex analysis, complex variables [PBKD], Real analysis, real variables [PBKB], Calculus & mathematical analysis [PBK], Mathematics [PB]