A note on rational Lp approximation
β Scribed by Andrew L Perrie
- Publisher
- Elsevier Science
- Year
- 1978
- Tongue
- English
- Weight
- 107 KB
- Volume
- 23
- Category
- Article
- ISSN
- 0021-9045
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
A convex function \(f\) given on \([-1,1]\) can be approximated in \(L_{r}, 1<p<x\). by convex polynomials \(P_{n}\) of degree at most \(n\) with the accuracy \(o\left(n^{-2 i p}\right)\). This follows from the estimate \(\left\|f-P_{n}\right\|_{p} \leqslant c \cdot n^{-2 / p} \cdot \omega_{2}^{\var
Let E be a subspace of C(X) and let R(E)= gΓh: g, h # E ; h>0]. We make a simple, yet intriguing observation: if zero is a best approximation to f from E, then zero is a best approximation to f from R(E ). We also prove that if That extends the results of P. Borwein and S. Zhou who proved it for t