Proceedings of the American Mathematical Society

Author(s): Marcin Bownik
Journal: Proc. Amer. Math. Soc. 137 (2009), 563-572.
MSC (2000): Primary 42C40
Posted: October 8, 2008
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Abstract: We prove that if the dimension function of a shift-invariant space

is not constantly $\infty$ , then the intersection of (negative) dilates of

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

DOI: 10.1090/S0002-9939-08-09682-2
PII: S 0002-9939(08)09682-2
Keywords: Shift-invariant space, refinable space, the dimension function, the spectral function, GMRA
Received by editor(s): December 20, 2007
Posted: October 8, 2008
Additional Notes: The author was partially supported by NSF grant DMS-0653881.
Communicated by: Michael T. Lacey
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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