Uniform approximation by incomplete polynomials

E. B. Saff and R. S. Varga

International Journal of Mathematics and Mathematical Sciences, 1978, vol. 1, 1-14

Abstract:

For any θ with 0 < θ < 1 , it is known that, for the set of all incomplete polynomials of type θ , i.e, { p ( x ) = ∑ k = s n a k x k : s ≥ θ ⋅ n } , to have the Weierstrass property on [ a θ , 1 ] , it is necessary that θ 2 ≤ a θ ≤ 1. In this paper, we show that the above inequalities are essentially sufficient as well.

Date: 1978
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:401670

DOI: 10.1155/S0161171278000411

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