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.

17 pages, 6 figures

References in corpus (9)

• Antisymmetric Orbit Functions
• Orthogonality within the Families of C-, S-, and E-Functions of Any Compact Semisimple Lie Group
• (Anti)symmetric multivariate trigonometric functions and corresponding Fourier transforms
• Orbit Functions
• On Discretization of Tori of Compact Simple Lie Groups II
• (Anti)symmetric multivariate exponential functions and corresponding Fourier transforms
• Four types of special functions of G_2 and their discretization
• Discrete Fourier analysis on a dodecahedron and a tetrahedron
• Six types of $E-$functions of the Lie groups O(5) and G(2)

Cited by in corpus (3)

• Generalized discrete orbit function transforms of affine Weyl groups
• Weight-Lattice Discretization of Weyl-Orbit Functions
• On immanant functions related to Weyl groups of $A_n$