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

Aldroubi, Akram; Sun, Qiyu

doi:10.1090/S0002-9939-02-06423-7

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

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