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, 155）
Cambridge University Press, 2014
2nd ed
- : hardback
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注記
Includes bibliographical references (p. [396]-412) and indexes
内容説明・目次
内容説明
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.
目次
- 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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