Please use this identifier to cite or link to this item: https://doi.org/10.1090/S0002-9939-06-08316-X
Title: Linear independence of pseudo-splines
Authors: Dong, B.
Shen, Z. 
Keywords: Linear independence
Pseudo-spline
Stability
Issue Date: Sep-2006
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
URI: http://scholarbank.nus.edu.sg/handle/10635/103495
ISSN: 00029939
DOI: 10.1090/S0002-9939-06-08316-X
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