Linear independence of pseudo-splines |
| |
Authors: | Bin Dong Zuowei Shen |
| |
Institution: | Department of Mathematics, National University of Singapore, Science Drive 2, Singapore 117543, Singapore ; Department of Mathematics, National University of Singapore, Science Drive 2, Singapore 117543, Singapore |
| |
Abstract: | In this paper, we show that the shifts of a pseudo-spline are linearly independent. This is stronger than the (more obvious) statement that the shifts of a pseudo-spline form a Riesz system. In fact, the linear independence of a compactly supported (refinable) function and its shifts has been studied in several areas of approximation and wavelet theory. Furthermore, the linear independence of the shifts of a pseudo-spline is a necessary and sufficient condition for the existence of a compactly supported function whose shifts form a biorthogonal dual system of the shifts of the pseudo-spline. |
| |
Keywords: | Linear independence pseudo-spline stability |
|
| 点击此处可从《Proceedings of the American Mathematical Society》浏览原始摘要信息 |
| 点击此处可从《Proceedings of the American Mathematical Society》下载免费的PDF全文 |
|