Orthogonal Algebraic Polynomial Schauder Bases of Optimal Degree

摘要

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.