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Abstract: Four families of special functions, depending on n variables, are studied. Wecall them symmetric and antisymmetric multivariate sine and cosine functions.They are given as determinants or antideterminants of matrices, whose matrixelements are sine or cosine functions of one variable each. These functions areeigenfunctions of the Laplace operator, satisfying specific conditions at theboundary of a certain domain F of the n-dimensional Euclidean space. Discreteand continuous orthogonality on F of the functions within each family, allowsone to introduce symmetrized and antisymmetrized multivariate Fourier-liketransforms, involving the symmetric and antisymmetric multivariate sine andcosine functions.



Author: A. Klimyk, J. Patera

Source: https://arxiv.org/



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