Local sampling theorems for spaces generated by splines with arbitrary knots

Sun, Wenchang

doi:10.1090/S0025-5718-08-02151-0

Local sampling theorems for spaces generated by splines with arbitrary knots
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by Wenchang Sun;

Math. Comp. 78 (2009), 225-239

DOI: https://doi.org/10.1090/S0025-5718-08-02151-0

Published electronically: June 25, 2008

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Abstract:

Most of the known results on sampling theorems, e.g., regular and irregular sampling theorems for band-limited functions, are concerned with global sampling. That is, to recover a function at a point or on an interval, we have to know all the samples, which are usually infinitely many. On the other hand, local sampling, which invokes only finitely many samples to reconstruct a function on a bounded interval, is practically useful since we only need to consider a function on a bounded interval in many cases and hardware can process only finitely many samples. In this paper, we give a characterization of local sampling sequences for spaces generated by B-splines with arbitrary knots.

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