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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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The refinability of step functions
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by Matthew J. Hirn PDF
Proc. Amer. Math. Soc. 136 (2008), 899-908 Request permission


Refinable functions have been widely investigated because of their importance in wavelet theory and multiresolution analysis, as well as because of intrinsic interest. Problems involving refinability can be challenging and interesting problems in mathematics. Several papers have investigated refinability of splines and other classes of functions. The purpose of this paper is to develop necessary and sufficient conditions for the refinability of the class of step functions on the real line taking complex values.
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Additional Information
  • Matthew J. Hirn
  • Affiliation: Department of Mathematics, Cornell University, Ithaca, New York
  • Address at time of publication: Department of Mathematics, University of Maryland, College Park, Maryland
  • Email:
  • Received by editor(s): July 20, 2004
  • Received by editor(s) in revised form: August 20, 2006
  • Published electronically: November 30, 2007
  • Communicated by: David R. Larson
  • © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 136 (2008), 899-908
  • MSC (2000): Primary 39B22
  • DOI:
  • MathSciNet review: 2361862