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Best polynomial approximation on the triangle

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Abstract

Let En(f)α,β,γ denote the error of best approximation by polynomials of degree at most n in the space L2(ϖα,β,γ) on the triangle {(x,y):x,y0,x+y1}, where ϖα,β,γ(x,y)xαyβ(1xy)γ for α,β,γ>1. Our main result gives a sharp estimate of En(f)α,β,γ in terms of the error of best approximation for higher order derivatives of f in appropriate Sobolev spaces. The result also leads to a characterization of En(f)α,β,γ by a weighted K-functional.

MSC

33C50
42C10

Keywords

Best polynomial approximation
Orthogonal expansion
Triangle
K-functional

Cited by (0)

1

The second author was supported in part by the Austrian Science Foundation FWF, grant SFB F50 (Special Research Program “Algorithmic and Enumerative Combinatorics”).

2

The third author was supported in part by NSF Grant DMS-1510296.