The discrete cosine transforms of types V--VIII are generalized to theantisymmetric and symmetric multivariate discrete cosine transforms. Fourfamilies of discretely and continuously orthogonal Chebyshev-like polynomialscorresponding to the antisymmetric and symmetric generalizations of cosinefunctions are introduced. Each family forms an orthogonal basis of the space ofall polynomials with respect to some weighted integral. Cubature formulas,which correspond to these families of polynomials and which stem from thedeveloped discrete cosine transforms, are derived. Examples ofthree-dimensional interpolation formulas and three-dimensional explicit formsof the polynomials are presented.
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