APPROXIMATING PALEY-WIENER FUNCTIONS BY SMOOTHED STEP FUNCTIONS

Authors
BEATY MG DODSON MM HIGGINS JR
Citation
Mg. Beaty et al., APPROXIMATING PALEY-WIENER FUNCTIONS BY SMOOTHED STEP FUNCTIONS, Journal of approximation theory, 78(3), 1994, pp. 433-445
Citations number
15
Categorie Soggetti
Mathematics, Pure",Mathematics
Journal title
Journal of approximation theory → ACNP
ISSN journal
00219045
Volume
78
Issue
3
Year of publication
1994
Pages
433 - 445
Database
ISI
SICI code
0021-9045(1994)78:3<433:APFBSS>2.0.ZU;2-7
Abstract
A function f with compactly supported Fourier transform can be approxi mated by a step function a which coincides with f at regularly spaced points sk, k epsilon Z. For suitable s, the functions f and a have the same L(2) norm. By modifying a so that its Fourier transform shares t he same compact support as that of f, an analytic function is obtained which approximates f, the accuracy depending on s. e 1994 Academic Pr ess, Inc.