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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Local sampling theorems for spaces generated by splines with arbitrary knots


Author: Wenchang Sun
Journal: Math. Comp. 78 (2009), 225-239
MSC (2000): Primary 65T40; Secondary 41A58, 42A65, 42C15, 94A20
Published electronically: June 25, 2008
MathSciNet review: 2448704
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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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Additional Information

Wenchang Sun
Affiliation: Department of Mathematics and LPMC, Nankai University, Tianjin 300071, China
Email: sunwch@nankai.edu.cn

DOI: http://dx.doi.org/10.1090/S0025-5718-08-02151-0
PII: S 0025-5718(08)02151-0
Keywords: Local sampling theorems, local sampling sequences, spline subspaces, irregular sampling, periodic nonuniform sampling
Received by editor(s): December 6, 2006
Received by editor(s) in revised form: October 25, 2007
Published electronically: June 25, 2008
Additional Notes: This work was supported partially by the National Natural Science Foundation of China (10571089 and 60472042), the Program for New Century Excellent Talents in Universities, and the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry.
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.