Revista de la
Unión Matemática Argentina
On convergence of subspaces generated by dilations of polynomials. An application to best local approximation
Fabián E. Levis and Claudia V. Ridolfi
Volume 61, no. 1 (2020), pp. 49–62

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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.