Abstract
When conducting a computing experiment on the extrapolation of the Fourier spectra of one-dimensional finite signals we used formula (30.4), with σ > 0 instead of —σ (see the remark in sec. 30). All computations were made with double precision. The first to be considered was the simple function f = (x -2 -2i)-1 ,belonging to the Hardy class H2 ,and points x k from the interval [0, 1]. For functions of this class formula (30.4) (with σ instead of -σ) is true for 0 < σ ≤ 2. It turned out that with σ -1/2, m = 22 the function f could be analytically continued with good accuracy (error less than 0.1) from [0, 1] onto [0, 30].
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© 1993 Springer Science+Business Media Dordrecht
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Aizenberg, L. (1993). Computing Experiment. In: Carleman’s Formulas in Complex Analysis. Mathematics and Its Applications, vol 244. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1596-4_9
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DOI: https://doi.org/10.1007/978-94-011-1596-4_9
Publisher Name: Springer, Dordrecht
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