Orthogonal polynomials of several variables
著者
書誌事項
Orthogonal polynomials of several variables
（Encyclopedia of mathematics and its applications / edited by G.-C. Rota, v. 81）
Cambridge University Press, 2001
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注記
Includes bibliographical references (p. 372-383) and indexes
内容説明・目次
内容説明
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.
目次
- 1. Background
- 2. Examples of orthogonal polynomials
- 3. General properties of orthogonal polynomials
- 4. Root systems and Coxeter groups
- 5. Spherical harmonics associated with reflection groups
- 6. Classical and generalized classical orthogonal polynomials
- 7. Summability of orthogonal polynomials
- 8. Orthogonal polynomials associated with symmetric groups
- 9. Orthogonal polynomials associated with octahedral groups
- 10. Bibliography
- Indexes.
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