A note on approximation by step functions
โ Scribed by Kazuaki Kitahara
- Publisher
- Elsevier Science
- Year
- 1990
- Tongue
- English
- Weight
- 231 KB
- Volume
- 3
- Category
- Article
- ISSN
- 0893-9659
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
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
By establishing an identity for \(S_{n}(x):=\sum_{j=0}^{n}|j / n-x|\left({ }_{j}^{n}\right) x^{j}(1-x)^{n-j}\), the present paper shows that a pointwise asymptotic estimate cannot hold for \(S_{n}(x)\), and, at the same time, obtains a better result than that in Bojanic and Cheng [3]. 1993 Academic