(Anti)symmetric multivariate trigonometric functions and corresponding Fourier transforms

Abstract

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.

25 pages, no figures; LaTaX; corrected typos

References in corpus (3)

• (Anti)symmetric multivariate exponential functions and corresponding Fourier transforms
• Properties of continuous Fourier extension of the discrete cosine transform and its multidimensional generalization
• Fourier transform method for imaging atmospheric Cherenkov telescopes

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• Discrete Fourier transform associated with generalized Schur polynomials
• Orthogonal polynomials of compact simple Lie groups
• Two dimensional symmetric and antisymmetric generalizations of sine functions
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• Four families of orthogonal polynomials of C2 and symmetric and antisymmetric generalizations of sine and cosine functions
• Four families of Weyl group orbit functions of B_3 and C_3
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• Three variable exponential functions of the alternating group