Four families of Weyl group orbit functions of B_3 and C_3

TL;DR

This paper studies four families of special functions related to B_3 and C_3 Lie groups, analyzing their properties and applications in Fourier expansions of digital 3D data sampled on lattices.

Contribution

It provides a detailed analysis of four families of Weyl group orbit functions and their use in Fourier expansions for 3D digital data.

Findings

Detailed properties of S^s- and S^l-functions for Fourier analysis.

Methods for digital data expansion on lattices of B_3 and C_3.

Examples of continuous interpolation of discrete expansions.

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.