Discrete Transforms and Orthogonal Polynomials of (Anti)Symmetric Multivariate Cosine Functions

@article{Hrivnk2014DiscreteTA,
  title={Discrete Transforms and Orthogonal Polynomials of (Anti)Symmetric Multivariate Cosine Functions},
  author={Jiř{\'i} Hrivn{\'a}k and Lenka Motlochov{\'a}},
  journal={SIAM J. Numer. Anal.},
  year={2014},
  volume={52},
  pages={3021-3055}
}
The discrete cosine transforms of types V--VIII are generalized to the antisymmetric and symmetric multivariate discrete cosine transforms. Four families of discretely and continuously orthogonal Chebyshev-like polynomials corresponding to the antisymmetric and symmetric generalizations of cosine functions are introduced. Each family forms an orthogonal basis of the space of all polynomials with respect to some weighted integral. Cubature formulas, which correspond to these families of… 
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