Jackson's theorem on complex arcs
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About: This article is published in Journal of Approximation Theory. The article was published on 01 Mar 1974. and is currently open access.
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Citations
Constructive description of certain classes of functions on quasismooth arcs
V V Andrievskiĭ,V V Maĭmeskul +1 more
- 28 Feb 1995
TL;DR: In this article, the structural properties of functions in these classes are described from a unified point of view, which allows one to understand more fully their nature and the differences between them.
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Jackson's inequality in the complex plane and the Łojasiewicz-Siciak inequality of Green's function
TL;DR: It is proved a generalization of Jackson's inequality for compact sets in the complex plane admitting both upper and lower bounds for their Green's functions, i.e., the well known Holder Continuity Property and the less known but crucial Łojasiewicz-Siciak inequality.
6
Polynomial approximation of polyharmonic functions on a complement of a John domain
TL;DR: A Jackson-Mergelyan type theorem is proved on the uniform polynomial approximation of continuous polyharmonic functions on a set "without cusps on the boundary that point inside of the set".
5
References
Lower bounds for the degree of approximation
TL;DR: In this paper, it was shown that standard means (trigonometric approximation, series of orthogonal polynomials) gives the best possible approximation, at least up to a bounded factor.
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