Shift-invariant spaces on the real line

Author:
Rong-Qing Jia

Journal:
Proc. Amer. Math. Soc. **125** (1997), 785-793

MSC (1991):
Primary 41A25, 41A15, 46E30

DOI:
https://doi.org/10.1090/S0002-9939-97-03586-7

MathSciNet review:
1350950

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Abstract | References | Similar Articles | Additional Information

Abstract: We investigate the structure of shift-invariant spaces generated by a finite number of *compactly supported* functions in . Based on a study of linear independence of the shifts of the generators, we characterize such shift-invariant spaces in terms of the semi-convolutions of the generators with sequences on . Moreover, we show that such a shift-invariant space provides -approximation order if and only if it contains all polynomials of degree less than .

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Additional Information

**Rong-Qing Jia**

Affiliation:
Department of Mathematics, University of Alberta, Edmonton, Canada T6G 2G1

Email:
jia@xihu.math.ualberta.ca

DOI:
https://doi.org/10.1090/S0002-9939-97-03586-7

Keywords:
Shift-invariant spaces,
approximation order

Received by editor(s):
April 13, 1995

Received by editor(s) in revised form:
August 10, 1995

Additional Notes:
The author was supported in part by NSERC Canada under Grant OGP 121336

Communicated by:
J. Marshall Ash

Article copyright:
© Copyright 1997
American Mathematical Society