Approximation from locally finite-dimensional

shift-invariant spaces

Author:
Kang Zhao

Journal:
Proc. Amer. Math. Soc. **124** (1996), 1857-1867

MSC (1991):
Primary 41A15, 41A25, 41A28, 41A63

DOI:
https://doi.org/10.1090/S0002-9939-96-03253-4

MathSciNet review:
1307577

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Abstract | References | Similar Articles | Additional Information

Abstract: After exploring some topological properties of locally finite-dimensional shift-invariant subspaces of , we show that if provides approximation order , then it provides the corresponding simultaneous approximation order. In the case is generated by a compactly supported function in , it is proved that provides approximation order in the -norm with if and only if the generator is a derivative of a compactly supported function that satisfies the Strang-Fix conditions.

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Additional Information

**Kang Zhao**

Affiliation:
Department of Mathematics, University of Utah, Salt Lake City, Utah 84112

Address at time of publication:
Structural Dynamics Research Corporation, 2000 Eastman Dr., Milford, Ohio 45150

Email:
kang.zhao@sdrc.com

DOI:
https://doi.org/10.1090/S0002-9939-96-03253-4

Keywords:
Approximation order,
locally finite-dimensional,
polynomial reproducing,
shift-invariant space,
simultaneous approximation,
Strang-Fix condition

Received by editor(s):
June 28, 1994

Received by editor(s) in revised form:
December 13, 1994

Communicated by:
J. Marshall Ash

Article copyright:
© Copyright 1996
American Mathematical Society