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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Reconstruction of functions in spline subspaces from local averages


Authors: Wenchang Sun and Xingwei Zhou
Journal: Proc. Amer. Math. Soc. 131 (2003), 2561-2571
MSC (2000): Primary 94A20; Secondary 42C40, 42C15
Published electronically: March 18, 2003
MathSciNet review: 1974656
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Abstract: In this paper, we study the reconstruction of functions in spline subspaces from local averages. We present an average sampling theorem for shift invariant subspaces generated by cardinal B-splines and give the optimal upper bound for the support length of averaging functions. Our result generalizes an earlier result by Aldroubi and Gröchenig.


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Additional Information

Wenchang Sun
Affiliation: Department of Mathematics, Nankai University, Tianjin 300071, People’s Republic of China
Email: sunwch@nankai.edu.cn

Xingwei Zhou
Affiliation: Department of Mathematics, Nankai University, Tianjin 300071, People’s Republic of China
Email: xwzhou@nankai.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-03-07082-5
PII: S 0002-9939(03)07082-5
Keywords: Average sampling, sampling theorems, spline subspaces
Received by editor(s): May 11, 2001
Published electronically: March 18, 2003
Additional Notes: This work was supported by the Research Fund for the Doctoral Program of Higher Education, the National Natural Science Foundation of China (Grant Nos. 10171050 and 10201014), the Mathematical Tianyuan Foundation(Grant No. TY10126007), and the Liuhui Center for Applied Mathematics
Communicated by: David R. Larson
Article copyright: © Copyright 2003 American Mathematical Society