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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Intersection of dilates of shift-invariant spaces
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by Marcin Bownik PDF
Proc. Amer. Math. Soc. 137 (2009), 563-572 Request permission

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
  • MR Author ID: 629092
  • Email: mbownik@uoregon.edu
  • 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
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 137 (2009), 563-572
  • MSC (2000): Primary 42C40
  • DOI: https://doi.org/10.1090/S0002-9939-08-09682-2
  • MathSciNet review: 2448576