Orthogonal Polynomials of Several Variables
2nd Edition
£129.00
Part of Encyclopedia of Mathematics and its Applications
- Authors:
- Charles F. Dunkl, University of Virginia
- Yuan Xu, University of Oregon
- Date Published: August 2014
- availability: Available
- format: Hardback
- isbn: 9781107071896
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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.
Read more- Incorporates classical and modern approaches
- Gives enough background information for readers to understand and apply symmetry techniques
- Covers in detail the families of orthogonal polynomials for important weight functions
Reviews & endorsements
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
See more reviewsReview 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 Society
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×Product details
- Edition: 2nd Edition
- Date Published: August 2014
- format: Hardback
- isbn: 9781107071896
- length: 426 pages
- dimensions: 240 x 159 x 28 mm
- weight: 0.81kg
- contains: 3 b/w illus.
- availability: Available
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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