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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.

MSC:

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

Citations:

Zbl 1142.41012
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Full Text: Euclid

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