Discretization of Generalized Chebyshev Polynomials of (Anti)symmetric Multivariate Sine Functions

Abstract

The multivariate antisymmetric and symmetric trigonometric functions allow to generalize the four kinds of classical Chebyshev polynomials to multivariate settings. The four classes of the bivariate polynomials, related to the symmetrized sine functions, are studied in detail. For each of these polynomials, the weighted continuous and discrete orthogonality relations are shown. The related cubature formulas for numerical integration together with further model examples and properties of selected special cases are discussed.