(Anti)symmetric multivariate trigonometric functions and corresponding Fourier transforms

Autor:	Klimyk, A., Patera, J.
Rok vydání:	2007
Předmět:	Mathematics - Classical Analysis and ODEs Mathematical Physics
Zdroj:	J. Math. Phys., vol. 48 (2007), 093504, 24 pages
Druh dokumentu:	Working Paper
DOI:	10.1063/1.2779768
Popis:	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. Comment: 25 pages, no figures; LaTaX; corrected typos
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/0705.4186 Zobrazit plný text záznamu View this record from Arxiv