Orthogonal polynomials of several variables / Charles F. Dunkl, Yuan Xu.

Format:

Book

Author/Creator:

Dunkl, Charles F., 1941- author.

Xu, Yuan, 1957- author.

Series:

Encyclopedia of mathematics and its applications ; v. 81.

Encyclopedia of mathematics and its applications ; volume 81

Language:

English

Subjects (All):

Orthogonal polynomials.

Functions of several real variables.

Physical Description:

1 online resource (xv, 390 pages) : digital, PDF file(s).

Place of Publication:

Cambridge : Cambridge University Press, 2001.

Language Note:

English

Summary:

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. The book will be welcomed by research mathematicians and applied scientists, including applied mathematicians, physicists, chemists and engineers.

Contents:

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.

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references (p. 372-383) and indexes.

ISBN:

1-139-88290-2

1-107-10140-9

1-107-10390-8

1-107-08951-4

0-511-56571-2

1-107-09582-4

1-107-09260-4

OCLC:

846202277