Two dimensional symmetric and antisymmetric generalizations of sine functions

Abstract

Properties of 2-dimensional generalizations of sine functions that are symmetric or antisymmetric with respect to permutation of their two variables are described. It is shown that the functions are orthogonal when integrated over a finite region $F$ of the real Euclidean space, and that they are discretely orthogonal when summed up over a lattice of any density in $F$. Decomposability of the products of functions into their sums is shown by explicitly decomposing products of all types. The formalism is set up for Fourier-like expansions of digital data over 2-dimensional lattices in $F$. Continuous interpolation of digital data is studied.

12 pages, 5 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 exponential and cosine 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 exponential and cosine functions
• Three variable exponential functions of the alternating group