Uniform approximation by incomplete polynomials
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....
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1978-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171278000411 |
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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |