Two-dimensional symmetric and antisymmetric generalizations of exponential and cosine functions

Abstract

Properties of the four families of recently introduced special functions of two real variables, denoted here by $E^{\pm }$, and ${\cos }^{\pm }$, are studied. The superscripts ${}^{+}$ and ${}^{-}$ refer to the symmetric and antisymmetric functions respectively. The functions are considered in all details required for their exploitation in Fourier expansions of digital data, sampled on square grids of any density and for general position of the grid in the real plane relative to the lattice defined by the underlying group theory. Quality of continuous interpolation, resulting from the discrete expansions, is studied, exemplified and compared for some model functions.

22 pages, 10 figures

References in corpus (3)

• (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 sine functions

Cited by in corpus (5)

• Generalized discrete orbit function transforms of affine Weyl groups
• Weight-Lattice Discretization of Weyl-Orbit Functions
• Discrete transforms and orthogonal polynomials of (anti)symmetric multivariate cosine functions
• Two dimensional symmetric and antisymmetric generalizations of sine functions
• Three variable exponential functions of the alternating group