Eigenfunctions of the 2D finite Fourier transform¹

Issue title: Computational and Mathematical Methods for Science and Engineering Conference 2002 – CMMSE-2002

Article type: Research Article

Authors: Larsson, B. | Levitina, T.^{; **} | Brändas, E.J.^{; *}

Affiliations: Department of Quantum Chemistry Uppsala University, Box 518, S-751 20 Uppsala, Sweden

Correspondence: [*] Corresponding author.

Note: [1] supported by the Royal Swedish Academy of Sciences, project number 12523, the Swedish Foundation for Strategic Research and the Russian Foundation for Basic Research under Grant No. 02-01-00050.

Note: [**] Permanent address: Institute for Computational Mathematics, TU Braunschweig, Pockelsstr. 14, D-38 106 Braunschweig, Germany.

Abstract: A new powerful approach to compute the eigenfunctions of the finite two-dimensional Fourier transform is developed and analysed. The numerical technique is a generalization of an earlier method developed for ordinary prolate spheroidal wave functions. Special considerations are given to the problem of singularities and the procedure to locate the eigenvalues. It is demonstrated that the computations are fundamentally improved by the introduction of appropriate auxiliary differential equations.

DOI: 10.3233/JCM-2004-41-216

Journal: Journal of Computational Methods in Sciences and Engineering, vol. 4, no. 1-2, pp. 135-148, 2004