(Anti)symmetric multivariate trigonometric functions and corresponding Fourier transforms

Understand

Four families of special functions, depending on n variables, are studied.

• We call them symmetric and antisymmetric multivariate sine and cosine functions.
• They are given as determinants or antideterminants of matrices, whose matrix elements are sine or cosine functions of one variable each.
• These functions are eigenfunctions of the Laplace operator, satisfying specific conditions at the boundary of a certain domain F of the n-dimensional Euclidean space.