Linear independence of pseudo-splines
Author:
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.
Publisher
American Mathematical Society (AMS)
Subject
Applied Mathematics,General Mathematics
Link
http://www.ams.org/proc/2006-134-09/S0002-9939-06-08316-X/S0002-9939-06-08316-X.pdf
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