Alternating multivariate trigonometric functions and corresponding Fourier transforms

被引:7
|
作者
Klimyk, A. U. [1 ]
Patera, J. [2 ]
机构
[1] Bogolyubov Inst Theoret Phys, UA-03680 Kiev, Ukraine
[2] Univ Montreal, Ctr Rech Math, Montreal, PQ H3C 3J7, Canada
关键词
D O I
10.1088/1751-8113/41/14/145205
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
We define and study multivariate sine and cosine functions, symmetric with respect to the alternating group An, 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.
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页数:16
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