Abstract
We develop discrete orthogonality relations on the finite sets of the generalized Chebyshev nodes related to the root systems A 2 , C 2 and G 2 . The orthogonality relations are consequences of orthogonality of four types of Weyl orbit functions on the fragments of the dual weight lattices. A uniform recursive construction of the polynomials as well as explicit presentation of all data needed for the discrete orthogonality relations allow practical implementation of the related Fourier methods. The polynomial interpolation method is developed and exemplified.
Highlights
The purpose of this article is to develop uniform explicit discrete orthogonality relations of ten types of bivariate generalized Chebyshev polynomials [1,2]
The discrete orthogonality relations are presented for two families of polynomials corresponding to the Lie algebra A2, and four, to the algebras C2 and G2
The four types of the current generalized Chebyshev polynomials corresponding to root systems of Weyl groups are induced by the four types of the Weyl orbit functions
Summary
The purpose of this article is to develop uniform explicit discrete orthogonality relations of ten types of bivariate generalized Chebyshev polynomials [1,2]. The polynomials of two continuous variables that are amenable to our discretization are those that are the ‘closest’ to the properties of finite dimensional irreducible representations of compact simple Lie groups of rank two, namely the groups of types A2 , C2 , and G2.
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