International Journal of Mathematics and Mathematical Sciences
Volume 1 (1978), Issue 4, Pages 407-420
doi:10.1155/S0161171278000411
Uniform approximation by incomplete polynomials
E.B. Saff1
and R.S. Varga2
1Department of Mathematics, University of South Florida, Tampa 33620, Florida, USA
2Department of Mathematics, Kent State University, Kent 44242, Ohio, USA
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=snakxk:s≥θ⋅n}, to have the Weierstrass property on [aθ,1], it is necessary that θ2≤aθ≤1. In this paper, we show that the above inequalities are essentially sufficient as well.