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Approximating Paley-Wiener Functions by Smoothed Step Functions

✍ Scribed by M.G. Beaty; M.M. Dodson; J.R. Higgins

Publisher: Elsevier Science
Year: 1994
Tongue: English
Weight: 339 KB
Volume: 78
Category: Article
ISSN: 0021-9045
DOI: 10.1006/jath.1994.1088

No coin nor oath required. For personal study only.

✦ Synopsis

A function (f) with compactly supported Fourier transform can be approximated by a step function (a) which coincides with (f) at regularly spaced points (s k, k \in \mathbb{Z}). For suitable (s), the functions (f) and (a) have the same (L^{2}) norm. By modifying (a) so that its Fourier transform shares the same compact support as that of (f), an analytic function is obtained which approximates (f), the accuracy depending on (s).

C 1994 Academic Press. Inc.

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