Intersection of dilates of shift-invariant spaces

Bownik, Marcin

doi:10.1090/S0002-9939-08-09682-2

Intersection of dilates of shift-invariant spaces
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by Marcin Bownik

Proc. Amer. Math. Soc. 137 (2009), 563-572

DOI: https://doi.org/10.1090/S0002-9939-08-09682-2

Published electronically: October 8, 2008

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Abstract:

We prove that if the dimension function of a shift-invariant space $V$ is not constantly $\infty$, then the intersection of (negative) dilates of $V$ must be trivial. We also give an example of two refinable shift-invariant spaces with identical spectral functions such that this intersection is either trivial or non-trivial.

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