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A method for computing the eigenvalues of prolate spheroidal functions of zero order. (English. Russian original) Zbl 1046.65114
Dokl. Math. 63, No. 1, 136-138 (2001); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 376, No. 1, 30-32 (2001).
From the introduction: We develop a new stable method for computing eigenvalues of the prolate spheroidal wave functions \(\psi_n(c,x)\) of order zero. The method computes eigenvalues with a high accuracy for any values of \(n\) and \(c\).
The prolate spheroidal wave functions of order zero are the eigenfunctions of the integral equation with a sinc kernel and of the Fourier transform. This allows their efficient use in many branches of science and engineering: the theory of antenna design, retrieval of objects from their images, ultrafine resolution, and resonator theory.
65R20 Numerical methods for integral equations
45C05 Eigenvalue problems for integral equations
33F05 Numerical approximation and evaluation of special functions
33E10 Lamé, Mathieu, and spheroidal wave functions
65D20 Computation of special functions and constants, construction of tables