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

Received 5 June 1978

Copyright © 1978 E. B. Saff and R. S. Varga. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.