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|Title:||Linear independence of pseudo-splines|
|Citation:||Dong, B., Shen, Z. (2006-09). Linear independence of pseudo-splines. Proceedings of the American Mathematical Society 134 (9) : 2685-2694. ScholarBank@NUS Repository. https://doi.org/10.1090/S0002-9939-06-08316-X|
|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. © 2006 American Mathematical Society.|
|Source Title:||Proceedings of the American Mathematical Society|
|Appears in Collections:||Staff Publications|
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