Abstract
Wilson bases are constituted by trigonometric functions multiplied by translates of a window function with good time frequency localization. In this article we investigate the approximation of functions from Sobolev spaces by partial sums of the Wilson basis expansion. In particular, we show that the approximation can be improved if polynomials are reproduced. We give examples of Wilson bases, which reproduce linear functions with the lowest-frequency term only.
| Original language | English |
|---|---|
| Pages (from-to) | 85-108 |
| Number of pages | 24 |
| Journal | Journal of Fourier Analysis and Applications |
| Volume | 8 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2002 |
| Externally published | Yes |
Keywords
- Biorthogonality
- Local trigonometric bases
- Riesz basis
- Unconditional bases
- Wilson bases