Orthogonal polynomials of several variables /Charles F. Dunkl, Yuan Xu.
- Cambridge ; New York : Cambridge University Press, (c)2001.
- 1 online resource (xv, 390 pages)
- Encyclopedia of mathematics and its applications ; volume 81 .
Includes bibliographies and index.
Examples of orthogonal polynomials in several bariables -- General properties of orthogonal polynomialsin several variables -- Root systems and coxeter groups -- Sperical harmonics associated with reflection groups -- Classical and generalized classical orthogonal polynomials -- Summability of orthogonal expansions -- Orthogonal polynomials associated with symmetric groups -- Orthogonal polynomials associated with octahedral groups and applications.
"This is the first modern book on orthogonal polynomials of several variables, which are interesting both as objects of study and as tools used in multivariate analysis, including approximations and numerical integration. The book, which is intended both as an introduction to the subject and as a reference, presents the theory in elegant form and with modern concepts and notation. It introduces the general theory and emphasizes the classical types of orthogonal polynomials whose weight functions are supported on standard domains such as the cube, the simplex, the sphere and the ball, or those of Gaussian type, for which fairly explicit formulae exist. The approach is a blend of classical analysis and symmetry-group-theoretic methods. Reflection groups are used to motivate and classify symmetries of weight functions and the associated polynomials. Many results come from current research literature. The book will be welcomed by research mathematicians and applied scientists, including applied mathematicians, physicists, chemists and engineers."--Jacket.
9781107089518 9780511565717 9781107095823
Orthogonal polynomials. Functions of several real variables.