Discrete Transforms and Orthogonal Polynomials of (Anti)symmetric Multivariate Sine Functions

  title={Discrete Transforms and Orthogonal Polynomials of (Anti)symmetric Multivariate Sine Functions},
  author={Adam Brus and Jiř{\'i} Hrivn{\'a}k and Lenka Motlochov{\'a}},
Sixteen types of the discrete multivariate transforms, induced by the multivariate antisymmetric and symmetric sine functions, are explicitly developed. Provided by the discrete transforms, inherent interpolation methods are formulated. The four generated classes of the corresponding orthogonal polynomials generalize the formation of the Chebyshev polynomials of the second and fourth kinds. Continuous orthogonality relations of the polynomials together with the inherent weight functions are… 
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Discrete Transforms and Orthogonal Polynomials of (Anti)Symmetric Multivariate Cosine Functions
Four families of discretely and continuously orthogonal Chebyshev-like polynomials corresponding to the antisymmetric and symmetric generalizations of cosine functions are introduced.
Two-dimensional symmetric and antisymmetric generalizations of sine functions
The properties of two-dimensional generalizations of sine functions that are symmetric or antisymmetric with respect to permutations of their two variables are described. It is shown that the
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