Three dimensional C-, S- and E-transforms

Abstract

Three dimensional continuous and discrete Fourier-like transforms, based on the three simple and four semisimple compact Lie groups of rank 3, are presented. For each simple Lie group, there are three families of special functions ($C$-, $S$-, and $E$-functions) on which the transforms are built. Pertinent properties of the functions are described in detail, such as their orthogonality within each family, when integrated over a finite region $F$ of the 3-dimensional Euclidean space (continuous orthogonality), as well as when summed up over a lattice grid $F_M\subset F$ (discrete orthogonality). The positive integer $M$ sets up the density of the lattice containing $F_M$. The expansion of functions given either on $F$ or on $F_M$ is the paper's main focus.

24 pages, 13 figures

References in corpus (4)

• E-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
• (Anti)symmetric multivariate exponential functions and corresponding Fourier transforms

Cited by in corpus (1)

• On Discretization of Tori of Compact Simple Lie Groups