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Discrete Orthogonality of Bivariate Polynomials of A2, C2 and G2

1
Department of Physics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Břehová 7, 115 19 Prague 1, Czech Republic
2
Centre de Recherches Mathématiques et Département de Mathématiques et de Statistique, Université de Montréal, C. P. 6128—Centre Ville, Montréal, QC H3C 3J7, Canada
3
Institute of Mathematics, University of Białystok, Ciołkowskiego 1M, 15-245 Białystok, Poland
*
Author to whom correspondence should be addressed.
Symmetry 2019, 11(6), 751; https://doi.org/10.3390/sym11060751
Received: 30 April 2019 / Revised: 27 May 2019 / Accepted: 28 May 2019 / Published: 3 June 2019
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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. View Full-Text
Keywords: orthogonal polynomial; discrete Fourier transform; Weyl group orthogonal polynomial; discrete Fourier transform; Weyl group
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Hrivnák, J.; Patera, J.; Szajewska, M. Discrete Orthogonality of Bivariate Polynomials of A2, C2 and G2. Symmetry 2019, 11, 751.

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