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Intersection of dilates of shift-invariant spaces


Author: Marcin Bownik
Journal: Proc. Amer. Math. Soc. 137 (2009), 563-572
MSC (2000): Primary 42C40
DOI: https://doi.org/10.1090/S0002-9939-08-09682-2
Published electronically: October 8, 2008
MathSciNet review: 2448576
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Abstract | References | Similar Articles | Additional Information

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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Additional Information

Marcin Bownik
Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon 97403–1222
Email: mbownik@uoregon.edu

DOI: https://doi.org/10.1090/S0002-9939-08-09682-2
Keywords: Shift-invariant space, refinable space, the dimension function, the spectral function, GMRA
Received by editor(s): December 20, 2007
Published electronically: October 8, 2008
Additional Notes: The author was partially supported by NSF grant DMS-0653881.
Communicated by: Michael T. Lacey
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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