An explicit solution of an \(L^ 1\) approximation problem (Q1060370)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: An explicit solution of an \(L^ 1\) approximation problem |
scientific article; zbMATH DE number 3907066
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An explicit solution of an \(L^ 1\) approximation problem |
scientific article; zbMATH DE number 3907066 |
Statements
An explicit solution of an \(L^ 1\) approximation problem (English)
0 references
1985
0 references
It is shown that \(\| 2^{1-n}T_ n\|_ 1=\int^{1}_{- 1}2^{1-n}| T_ n(x)| dx/\sqrt{1-x^ 2}<\| p_ n\|_ 1\) where \(T_ n\) is the nth degree Chebyshev polynomial of the first kind and \(p_ n\) is any other monic polynomial of degree n.
0 references
Chebyshev polynomial
0 references
