Abstract. 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.

PACS numbers: 02.10.Gd, 02.20.-a, 02.30.Gp, 02.30.Nw, 02.60.Lj

Print publication: Issue 14 (11 April 2008)
Received 3 January 2008, in final form 25 February 2008
Published 26 March 2008