Proceedings of the American Mathematical Society

Author(s): Akram Aldroubi; Qiyu Sun
Journal: Proc. Amer. Math. Soc. 130 (2002), 2641-2654.
MSC (2000): Primary 42C40, 46A35, 46E15
Posted: February 12, 2002
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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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Akram Aldroubi
Affiliation: Department of Mathematics, Vanderbilt University, Nashville, Tennnessee 37240
Email: aldroubi@math.vanderbilt.edu

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