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## Online first articles

Articles are posted here individually soon after proof is returned from authors, before the corresponding journal issue is completed. All articles are in their final form, including issue number and pagination. For recently accepted articles, see Articles in press.

#### Vol. 61, no. 1 (2020)

 Local solvability of elliptic equations of even order with Hölder coefficients. María Amelia Muschietti and Federico Tournier We consider elliptic equations of order $2m$ with Hölder coefficients. We show local solvability of the Dirichlet problem with $m$ conditions on the boundary of the upper half space. First we consider local solvability in free space and then we treat the boundary case. Our method is based on applying the operator to an approximate solution and iterating in the Hölder spaces. A priori estimates for the approximate solution is the essential part of the paper. 1–47 On convergence of subspaces generated by dilations of polynomials. An application to best local approximation. Fabián E. Levis and Claudia V. Ridolfi We study the convergence of a net of subspaces generated by dilations of polynomials in a finite dimensional subspace. As a consequence, we extend the results given by Zó and Cuenya [Advanced Courses of Mathematical Analysis II (Granada, 2004), 193–213, World Scientific, 2007] on a general approach to the problems of best vector-valued approximation on small regions from a finite dimensional subspace of polynomials. 49–62