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[ 洋図書 ] Orthogonal polynomials of several variables / ( Encyclopedia of mathematics and its applications ; 155 )

Charles F. Dunkl, Yuan Xu. -- Cambridge University Press, -- 2014. -- 2nd ed.

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ISBN 1107071895
ISBN13桁 9781107071896
テキストの言語 英語                  
分類：NDC10版 410.8
個人著者標目 Dunkl, Charles F.,
生没年等 1941-
本タイトル Orthogonal polynomials of several variables /
著者名 Charles F. Dunkl, Yuan Xu.
版表示 2nd ed.
出版地・頒布地 Cambridge :
出版者・頒布者名 Cambridge University Press,
出版年・頒布年 2014.
数量 xvii, 420 p. :
他の形態的事項 ill. ;
大きさ 25 cm.
書誌注記 Includes bibliographical references (p. [396]-412) and indexes.
内容注記 1. Background -- The gamma and beta functions -- Hypergeometric series -- Orthogonal polynomials of one variable -- Classical orthogonal polynomials -- Modified classical polynomials -- Notes -- 2. Orthogonal polynomials in two variables -- Introduction -- Product orthogonal polynomials -- Orthogonal polynomials on the unit disk -- Orthogonal polynomials on the triangle -- Orthogonal polynomials and differential equations -- Generating orthogonal polynomials of two variables -- First family of koornwinder polynomials -- A related family of orthogonal polynomials -- Second family of koornwinder polynomials -- 3. General properties of orthogonal polynomials in several variables -- Notation and preliminaries -- Moment funtionals and orthogonal polynomials -- The three-term relation -- Jacobi matrices and commuting operators -- Further properties of the three-term relation -- Reproducing kernels and fourier orthogonal series -- Common zeros of orthogonal polynomials in several variables -- Gaussian cubature formulae -- Notes -- 4. Orthogonal polynomials on the unit sphere -- Spherical harmonics -- Orthoginal structures on Sd and on Bd -- Orthogonal structures on Bd and on Sd+m-1 -- Orthogonal structure on the simplex -- Van der corput -- Schaake inequality -- 5. Examples of orthogonal polynomials in several variables -- Orthogonal polynomials for simple weight functions -- Classical orthogonal polynomials on the unit ball -- Classical orthogonal polynomials on the simplex -- Orthogonal polynomials via symmetric functions -- Chebyshev polynomials to Type Ad -- Sobolev orthogonal polynomials on the unit ball -- 6. Root systems and coxeter groups -- Introduction and overview -- Root systems -- Invariant polynomials -- Differential-difference operators -- The intertwining operator -- The K-analogue of the exponential -- Invariant differential operators -- 7. Spherical harmonics associated with reflection groups -- h-Harmonic polynomials -- Inner products on polynomials -- Reproducing kernels and the poisson kernel -- Integration of the intertwining operator -- Example: Abelian group Z d/2 -- Example: Dihedral groups -- The dunk1 transform -- 8. Generalized classical orthogonal polynomials -- Generalized classical orthogonal polynomials on the ball -- Generalized classical orthogonal polynomials on the simplex -- Generalized hermite polynomials -- Generalized laguerre polynomials -- 9. Summability of orthogonal expansions -- General results on orthogonal expansions -- Orthogonal expansion on the sphere -- Orthogonal expansion on the ball -- Orthogonal expansion on the simplex -- Orthogonal expansion of Laguerre and Hermite polynomials -- Multiple Jacobi expansion -- 10. Orthogonal polynomials associated with symmetric groups -- Partitions, compositions and orderings -- Commuting self-adjoint operators -- The dual polynomials basis -- Sd-invariant subspaces -- Degree-changing recurrences -- Norm formulae -- Symmetric functions and jack polynomials -- Miscellaneous topics -- 11. Orthogonal polynomials associated with octahedral groups, and applications -- Operators of Type B -- Polynomial eigenfunctions of Type B -- Generalized binomial coefficients -- Hermite polynomials of Type B -- Calogero-Sutherland systems.
著者標目 Xu, Yuan, 1957-
統一タイトル(シリーズ副出標目) Encyclopedia of mathematics and its applications ;
シリーズの巻次 155.
シリーズ名・巻次 Encyclopedia of mathematics and its applications ; 155
一般件名 Orthogonal polynomials.
Functions of several real variables.
資料情報1 『Orthogonal polynomials of several variables /』（Encyclopedia of mathematics and its applications ; 155）2nd ed.　Charles F. Dunkl, Yuan Xu.　Cambridge University Press,　2014. （所蔵館：中央　 請求記号：F/410.8/E56/E1-155　 資料コード：7104875500）
URL https://catalog.library.metro.tokyo.lg.jp/winj/opac/switch-detail.do?lang=ja&bibid=1352012259

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