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....
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
1978-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171278000411 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832563350946447360 |
|---|---|
| author | E. B. Saff R. S. Varga |
| author_facet | E. B. Saff R. S. Varga |
| author_sort | E. B. Saff |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-360548e990c84be295ea490da5f6f44a |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1978-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-360548e990c84be295ea490da5f6f44a2025-02-03T01:20:18ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251978-01-011440742010.1155/S0161171278000411Uniform approximation by incomplete polynomialsE. B. Saff0R. S. Varga1Department of Mathematics, University of South Florida, Tampa 33620, Florida, USADepartment of Mathematics, Kent State University, Kent 44242, Ohio, USAFor 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.http://dx.doi.org/10.1155/S0161171278000411incomplete polynomialsWeierstrass propertyuniform convergence. |
| spellingShingle | E. B. Saff R. S. Varga Uniform approximation by incomplete polynomials International Journal of Mathematics and Mathematical Sciences incomplete polynomials Weierstrass property uniform convergence. |
| title | Uniform approximation by incomplete polynomials |
| title_full | Uniform approximation by incomplete polynomials |
| title_fullStr | Uniform approximation by incomplete polynomials |
| title_full_unstemmed | Uniform approximation by incomplete polynomials |
| title_short | Uniform approximation by incomplete polynomials |
| title_sort | uniform approximation by incomplete polynomials |
| topic | incomplete polynomials Weierstrass property uniform convergence. |
| url | http://dx.doi.org/10.1155/S0161171278000411 |
| work_keys_str_mv | AT ebsaff uniformapproximationbyincompletepolynomials AT rsvarga uniformapproximationbyincompletepolynomials |