Multivariate Chebyshev polynomials

作者：Lyakhovsky V D^*; Uvarov Ph V

来源：Journal of Physics A-Mathematical and Theoretical, 2013, 46(12): 125201.

DOI：10.1088/1751-8113/46/12/125201

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).

• 出版日期2013-3-29