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

 

Partitions of unity and approximation


Authors: C. de Boor and R. DeVore
Journal: Proc. Amer. Math. Soc. 93 (1985), 705-709
MSC: Primary 41A15
MathSciNet review: 776207
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Abstract: We show that for certain translation invariant spaces $ S$, a necessary and sufficient condition for the eventual denseness of the corresponding scaled spaces $ {S_h}$ is that $ S$ contain a stable and locally supported partition of unity. These results have been motivated by recent work on approximation by multivariate piecewise polynomials on regular meshes.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0776207-2
PII: S 0002-9939(1985)0776207-2
Keywords: Degree of approximation, partition of unity, piecewise polynomial
Article copyright: © Copyright 1985 American Mathematical Society