Reconstruction of functions in spline subspaces from local averages

Sun, Wenchang; Zhou, Xingwei

doi:10.1090/S0002-9939-03-07082-5

Reconstruction of functions in spline subspaces from local averages
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by Wenchang Sun and Xingwei Zhou

Proc. Amer. Math. Soc. 131 (2003), 2561-2571

DOI: https://doi.org/10.1090/S0002-9939-03-07082-5

Published electronically: March 18, 2003

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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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