Locally finite dimensional shift-invariant spaces in ![]() |
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| Authors: | Akram Aldroubi Qiyu Sun |
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| Affiliation: | Department of Mathematics, Vanderbilt University, Nashville, Tennnessee 37240 ; Department of Mathematics, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Singapore |
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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  or the fractional Sobolev space  , then the superspace can be chosen to be  or  , respectively. |
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| Keywords: | Fractional Sobolev spaces, H" older continuous, distributions |
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