Locally finite dimensional shift-invariant spaces in $\mathbf {R}^d$
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- by Akram Aldroubi and Qiyu Sun PDF
- Proc. Amer. Math. Soc. 130 (2002), 2641-2654 Request permission
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.References
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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
- 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
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 2641-2654
- MSC (2000): Primary 42C40, 46A35, 46E15
- DOI: https://doi.org/10.1090/S0002-9939-02-06423-7
- MathSciNet review: 1900872