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A counterexample to a result concerning controlled approximation


Author: Rong Qing Jia
Journal: Proc. Amer. Math. Soc. 97 (1986), 647-654
MSC: Primary 41A15; Secondary 41A45
DOI: https://doi.org/10.1090/S0002-9939-1986-0845982-1
MathSciNet review: 845982
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Abstract: A result of Strang and Fix states that if the order of controlled approximation from a collection of locally supported elements is $ k$, then there is a linear combination $ \Omega $ of those elements and their translates such that any polynomial of degree less than $ k$ can be reproduced by $ \Omega $ and its translates. This paper gives a counterexample to their result.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1986-0845982-1
Article copyright: © Copyright 1986 American Mathematical Society

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