We present a general approach to obtain direct and inverse results for approximation in Hölder norms. This approach is used to obtain a collection of new results related with estimates of the best polynomial approximation and with the approximation by linear operators of non-periodic functions in Hölder norms.
A universality theorem for ratios of random characteristic polynomials Original Research Article Pages 803-814 Stolz angle limit of a certain class of self-mappings of the unit disk Original Research Article Pages 815-822 A generalization of the Riesz–Fischer theorem and linear summability methods Original Research Article Pages 841-853
We improve the class of indices for which normality takes place in a Nikishin system and apply this in Hermite-Padé approximation of such systems of functions.
For a given θ ∈ (a, b), we investigate the question whether there exists a positive quadrature formula with maximal degree of precision which has the prescribed abscissa θ plus possibly a and/or b, the endpoints of the interval of integration. This study relies on recent results on the location of roots of quasi-orthogonal polynomials. The above positive… (More)
This paper is an introductory approach to several approximation problems of periodic functions in connection with Fourier series, Lipschitz functions and related topics. Traditional results in this context are presented and discussed in the first two sections. Further, we introduce certain Hölder spaces of integrable functions that become homogeneous Banach… (More)