Abstract
We construct bounded polynomial operators, similar to the classical de la Vallée Poussin operators in the theory of Fourier series, which preserve polynomials of a certain degree, but are defined in terms of the values of the function rather than its Fourier coefficients.
| Original language | English |
|---|---|
| Journal | Journal of Approximation Theory |
| Volume | 96 |
| Issue number | 1 |
| Pages (from-to) | 67-85 |
| Number of pages | 19 |
| ISSN | 0021-9045 |
| DOIs | |
| Publication status | Published - 01.01.1999 |
Funding
We are grateful to Doron Lubinsky for his generous help in improving the first draft of this paper. This research was supported, in part, by National Science Foundation Grant DMS 9404513, Air Force Office of Scientific Research Grant F49620-97-1-0211, and the Alexander von Humboldt Foundation.