Description
Book SynopsisServing both as an introduction to the subject and as a reference, this book covers the general theory and emphasizes the classical types of orthogonal polynomials, or those of Gaussian type. Containing 25% brand new material, this revised edition reflects progress made in the field over the past decade.
Trade ReviewReview 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 Society
Table of ContentsPreface 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.
