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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Locally finite dimensional shift-invariant spaces in $\mathbf{R}^d$


Authors: Akram Aldroubi and Qiyu Sun
Journal: Proc. Amer. Math. Soc. 130 (2002), 2641-2654
MSC (2000): Primary 42C40, 46A35, 46E15
Published electronically: February 12, 2002
MathSciNet review: 1900872
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Abstract: We prove that a locally finite dimensional shift-invariant linear space of distributions must be a linear subspace of some shift-invariant space generated by finitely many compactly supported distributions. If the locally finite dimensional shift-invariant space is a subspace of the Hölder continuous space $C^\alpha$ or the fractional Sobolev space $L^{p, \gamma}$, then the superspace can be chosen to be $C^\alpha$ or $L^{p, \gamma}$, respectively.


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Additional Information

Akram Aldroubi
Affiliation: Department of Mathematics, Vanderbilt University, Nashville, Tennnessee 37240
Email: aldroubi@math.vanderbilt.edu

Qiyu Sun
Affiliation: Department of Mathematics, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Singapore
Email: matsunqy@nus.edu.sg

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06423-7
PII: S 0002-9939(02)06423-7
Keywords: Fractional Sobolev spaces, H\"older continuous, distributions
Received by editor(s): October 27, 2000
Received by editor(s) in revised form: April 2, 2001
Published electronically: February 12, 2002
Additional Notes: The first author’s research was supported in part by NSF grant DMS-9805483.
Communicated by: David R. Larson
Article copyright: © Copyright 2002 American Mathematical Society