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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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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Shift-invariant spaces on the real line
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by Rong-Qing Jia PDF
Proc. Amer. Math. Soc. 125 (1997), 785-793 Request permission

Abstract:

We investigate the structure of shift-invariant spaces generated by a finite number of compactly supported functions in $L_p(\mathbb {R})$ $(1\le p\le \infty )$. 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 $\mathbb {Z}$. Moreover, we show that such a shift-invariant space provides $L_p$-approximation order $k$ if and only if it contains all polynomials of degree less than $k$.
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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
  • 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
  • © Copyright 1997 American Mathematical Society
  • 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