Discretization of four types of Weyl group orbit functions

Hrivnák, Jiří

doi:10.1088/1742-6596/474/1/012021

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Discrete Orthogonality Of a 2 Polynomials1

Introduction1

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2019

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“…The coordinates of the points Z j in the sets F M and F M are obtained by using the functions (18), (19) into substitution (29). The sets F M and F M are for M = 6 and M = 12 depicted in Figure 1.…”

Section: Discrete Orthogonality Of a 2 Polynomialsmentioning

confidence: 99%

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Discrete Orthogonality of Bivariate Polynomials of A2, C2 and G2

2019

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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.

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Section: Discrete Orthogonality Of a 2 Polynomialsmentioning

confidence: 99%

“…The discrete orthogonality relations of the polynomials are induced by the orthogonality of the underlying Weyl orbit functions. Several discretizations of the Weyl orbit functions are currently known [18][19][20][21][22]. Dual weight lattice discretization of the orbit functions, used in this paper, is presented in all details in [19,21].…”

Section: Introductionmentioning

confidence: 99%