T. Kilgore, J. Prestin, K. Selig
Orthogonal Algebraic Polynomial Schauder Bases of Optimal Degree
Preprint series: Preprints aus dem Fachbereich Mathematik, Universität Rostock

MSC:

41A05 Interpolation, See also {42A15 and 65D05}

41A10 Approximation by polynomials, {For approximation by trigonometric polynomials, See 42A10}

Abstract: For any fixed $\varepsilon > 0$ we construct an orthonormal
Schauder basis $\{p_\mu\}_{\mu=0}^{\infty}$ for $C[-1,1]$
consisting of algebraic polynomials $p_\mu$ with
$\deg p_\mu \le (1+\varepsilon) \mu $. \\
The orthogonality is with respect to the Chebyshev weight.
Keywords: Schauder Basis, Polynomial Wavelets, Chebyshev Polynomials, Optimal degree