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Proceedings of the American Mathematical Society

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The refinability of step functions

Author: Matthew J. Hirn
Journal: Proc. Amer. Math. Soc. 136 (2008), 899-908
MSC (2000): Primary 39B22
Published electronically: November 30, 2007
MathSciNet review: 2361862
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Abstract: 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

Keywords: Refinable equations, step function
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
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.