(Anti)symmetric multivariate trigonometric functions and corresponding Fourier transforms

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

2007-05-29

arxiv.org/abs/0705.4186v2

J. Math. Phys., vol. 48 (2007), 093504, 24 pages

Mathematics

Classical Analysis and ODEs

25 pages, no figures; LaTaX; corrected typos

Scientific paper

10.1063/1.2779768

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. Discrete and continuous orthogonality on F of the functions within each family, allows one to introduce symmetrized and antisymmetrized multivariate Fourier-like transforms, involving the symmetric and antisymmetric multivariate sine and cosine functions.

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