Three variable exponential functions of the alternating group

Abstract

New class of special functions of three real variables, based on the alternating subgroup of the permutation group $S_3$, is studied. These functions are used for Fourier-like expansion of digital data given on lattice of any density and general position. Such functions have only trivial analogs in one and two variables; a connection to the $E-$functions of $C_3$ is shown. Continuous interpolation of the three dimensional data is studied and exemplified.

10 pages, 3 figures

References in corpus (4)

• (Anti)symmetric multivariate trigonometric functions and corresponding Fourier transforms
• (Anti)symmetric multivariate exponential functions and corresponding Fourier transforms
• Two-dimensional symmetric and antisymmetric generalizations of exponential and cosine functions
• Two dimensional symmetric and antisymmetric generalizations of sine functions