Orthogonal polynomial Schauder bases in \(C[-1,1]\) with optimal growth of degrees (Q2759318)
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: Orthogonal polynomial Schauder bases in \(C[-1,1]\) with optimal growth of degrees |
scientific article; zbMATH DE number 1681722
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Orthogonal polynomial Schauder bases in \(C[-1,1]\) with optimal growth of degrees |
scientific article; zbMATH DE number 1681722 |
Statements
3 January 2002
0 references
polynomial Schauder basis
0 references
multiresolution analysis
0 references
orthonormal basis
0 references
Orthogonal polynomial Schauder bases in \(C[-1,1]\) with optimal growth of degrees (English)
0 references
The author proves in a constructive way, based on ideas of \textit{R. A. Lorentz} and \textit{A. A. Sahakian} [J. Fourier Anal. Appl. 1, No. 1, 103-112 (1994; Zbl 0839.42013)], that for each \(\varepsilon> 0\) there exists a sequence of algebraic polynomials of degree at most \(n(1+\varepsilon)\) (= lowest possible degree) that are orthogonal on \([-1,1]\) (weight \(\equiv 1\)) and form a Schauder basis of the space \(C[-1,1]\).
0 references
