Klimyk, A. U.; Patera, J. Alternating multivariate trigonometric functions and corresponding Fourier transforms. (English) Zbl 1183.33027 J. Phys. A, Math. Theor. 41, No. 14, Article ID 145205, 16 p. (2008). Summary: We define and study multivariate sine and cosine functions, symmetric with respect to the alternating group \(A_n\), which is a subgroup of the permutation (symmetric) group \(S_n\). These functions are eigenfunctions of the Laplace operator. They determine Fourier-type transforms. There exist three types of such transforms: expansions into corresponding sine-Fourier and cosine-Fourier series, integral sine-Fourier and cosine-Fourier transforms, and multivariate finite sine and cosine transforms. In all these transforms, alternating multivariate sine and cosine functions are used as a kernel. Cited in 2 Documents MSC: 33C80 Connections of hypergeometric functions with groups and algebras, and related topics 42B10 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type Keywords:multivariate sine function; multivariate cosine function; Fourier-type transforms PDFBibTeX XMLCite \textit{A. U. Klimyk} and \textit{J. Patera}, J. Phys. A, Math. Theor. 41, No. 14, Article ID 145205, 16 p. (2008; Zbl 1183.33027) Full Text: DOI