%0 Journal Article %T Polynomial operators and local smoothness classes on the unit interval, II %A H. N. Mhaskar %J Mathematics %D 2008 %I arXiv %X We prove the existence of quadrature formulas exact for integrating high degree polynomials with respect to Jacobi weights based on scattered data on the unit interval. We also obtain a characterization of local Besov spaces using the coefficients of a tight frame expansion. %U http://arxiv.org/abs/0811.2594v1