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On the degree of approximation by step functions

✍ Scribed by O Shisha


Publisher
Elsevier Science
Year
1974
Tongue
English
Weight
91 KB
Volume
12
Category
Article
ISSN
0021-9045

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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 Fou