(Anti)symmetric multivariate exponential functions and corresponding Fourier transforms

Details (Anti)symmetric multivariate exponential functions and corresponding Fourier transforms (Anti)symmetric multivariate exponential functions and corresponding Fourier transforms

2007-05-24

arxiv.org/abs/0705.3572v1

Mathematics

Classical Analysis and ODEs

18 pages, no figeres

Scientific paper

10.1088/1751-8113/40/34/006

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. There are three types of such Fourier transforms: expansions into corresponding Fourier series, integral Fourier transforms, and multivariate finite Fourier transforms. Eigenfunctions of the integral Fourier transforms are found.

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