Multivariate Chebyshev polynomials

被引：8

作者：

Lyakhovsky, V. D. ^{[1
]}

Uvarov, Ph V. ^{[2
]}

机构：

[1] St Petersburg State Univ, High Energy Phys & Elementary Particles Dept, St Petersburg 198904, Russia

[2] St Petersburg State Univ, Chebyshev Lab, St Petersburg 198904, Russia

来源：

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL | 2013年 / 46卷 / 12期

关键词：

D O I：

10.1088/1751-8113/46/12/125201

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We study multivariate Chebyshev polynomials associated with root systems. Using properties of specialized singular elements Phi(;alpha)(g) corresponding to a root system Delta(g), we construct explicitly the measure weight function gamma. The latter ensures that these polynomials are orthonormal; it defines the scalar product in the function space L-2 (F, gamma) where multivariate U-type Chebyshev polynomials U-g(mu) constitute a basis. The obtained results are illustrated by constructing and studying 2-variate polynomials U-g(mu) for root systems Delta(A2), Delta(B2) and Delta(G2).

引用

页数：22