Four families of Weyl group orbit functions of B_3 and C_3

Abstract

The properties of the four families of special functions of three real variables, called here C-, S-, S^s- and S^l-functions, are studied. The S^s- and S^l-functions are considered in all details required for their exploitation in Fourier expansions of digital data, sampled on finite fragment of lattices of any density and of the 3D symmetry imposed by the weight lattices of B_3 and C_3 simple Lie algebras/groups. The continuous interpolations, which are induced by the discrete expansions, are exemplified and compared for some model functions.