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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Controlled approximation and a characterization of the local approximation order
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by C. de Boor and R.-Q. Jia PDF
Proc. Amer. Math. Soc. 95 (1985), 547-553 Request permission

Abstract:

The local approximation order from a scale $({S_h})$ of approximating functions on ${{\mathbf {R}}^m}$ is characterized in terms of the linear span (and its Fourier transform) of the finitely many compactly supported functions $\varphi$ whose integer translates $\varphi ( \cdot - j),j \in {z^m}$, span the space $S = {S_1}$ from which the scale is derived. This provides a correction of similar results stated and proved, in part, by Strang and Fix.
References
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Additional Information
  • © Copyright 1985 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 95 (1985), 547-553
  • MSC: Primary 41A25; Secondary 65N30
  • DOI: https://doi.org/10.1090/S0002-9939-1985-0810161-X
  • MathSciNet review: 810161