A U Klimyk and J Patera 2008 J. Phys. A: Math. Theor. 41 145205 doi:10.1088/1751-8113/41/14/145205
Alternating multivariate trigonometric functions and corresponding Fourier transforms
A U Klimyk1 and J Patera2
Show affiliationsWe 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 Sn. 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
- MSC
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42A05 Trigonometric polynomials, inequalities, extremal problems
42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
47D09 Operator sine and cosine functions and higher-order Cauchy problems (See also 34G10)
- Subjects
- Dates
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Issue 14 (11 April 2008)
Received 3 January 2008, in final form 25 February 2008
Published 26 March 2008
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Alternating multivariate trigonometric functions and corresponding Fourier transforms
A U Klimyk and J Patera 2008 J. Phys. A: Math. Theor. 41 145205
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