(Anti)symmetric multivariate exponential functions and corresponding Fourier transforms

Understand

We define and study symmetrized and antisymmetrized multivariate exponential functions.

• They are defined as determinants and antideterminants of matrices whose entries are exponential functions of one variable.
• These functions are eigenfunctions of the Laplace operator on corresponding fundamental domains satisfying certain boundary conditions.
• To symmetric and antisymmetric multivariate exponential functions there correspond Fourier transforms.