Approximation from locally finitedimensional shiftinvariant spaces
Author:
Kang Zhao
Journal:
Proc. Amer. Math. Soc. 124 (1996), 18571867
MSC (1991):
Primary 41A15, 41A25, 41A28, 41A63
MathSciNet review:
1307577
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Abstract: After exploring some topological properties of locally finitedimensional shiftinvariant 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 StrangFix 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:
http://dx.doi.org/10.1090/S0002993996032534
PII:
S 00029939(96)032534
Keywords:
Approximation order,
locally finitedimensional,
polynomial reproducing,
shiftinvariant space,
simultaneous approximation,
StrangFix 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
