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Generalized Stieltjes polynomials are introduced and their asymptotic properties outside the support of the measure are studied. As applications, we prove the convergence of sequences of interpolating rational functions, whose poles are partially fixed, to Markov functions and give an asymptotic estimate of the error of rational GaussKronrod quadrature formulas when functions which are analytic on...
We characterize the approximation spaces associated with the best n-term approximation in Lp(R) by elements from a tight wavelet frame associated with a spline scaling function. The approximation spaces are shown to be interpolation spaces between Lp and classical Besov spaces, and the result coincides with the result for nonlinear approximation with an orthonormal wavelet with the same smoothness...
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