Best local weighted approximation. An approach with abstract seminorms. (English) Zbl 1444.41008

Summary: We extend results given by F. Zó and H. H. Cuenya, in [Proceedings of the 2nd international school “Advanced courses of mathematical analysis 2”, Granada, Spain, September 20–24, 2004. Hackensack, NJ: World Scientific. 193–213 (2007; Zbl 1142.41012)] about a general approach to problems of best vector-valued approximation on small regions from a finite dimensional subspace of polynomials of some degree. This approach is called best local approximation. We consider a weighted local approximation of a vector-valued function on the origin and a weighted best local approximation of a real-valued function on several points, similar to classical problems in best local approximation with balanced neighborhood.


41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
41A10 Approximation by polynomials
42A10 Trigonometric approximation


Zbl 1142.41012
Full Text: Euclid


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