Orthogonal algebraic polynomial Schauder bases of optimal degree (Q1357301)

For any fixed \(\varepsilon >0\), the paper presents an orthogonal algebraic polynomial Schauder basis \(\{ p_{\mu} \}_{\mu=0}^{\infty}\) of optimal degree \(\text{ deg} p_{\mu} \leq (1+ \varepsilon) \mu\). The construction method is based on adapted wavelet techniques, in particular adapted wavelet packets. Orthogonality is given with respect to the weighted inner product \[ \langle f, g \rangle = {2 \over \pi} \int_{-1}^1 f(x) g(x) { \text{ d} x \over \sqrt{1-x^2}}. \] The orthogonal algebraic polynomials \(p_{\mu}\) are explicitly described in terms of their Chebyshev expansions.