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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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Local dual and poly-scale refinability
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by Qiyu Sun PDF
Proc. Amer. Math. Soc. 133 (2005), 1175-1184 Request permission

Abstract:

For a compactly supported function $f$, let $S_n(f), n\ge 0$, be the space of all finite linear combinations of $f(M^n\cdot -k), k\in \mathbf Z$. In this paper, we consider the explicit construction of local duals of $f$ and the poly-scale refinability of functions in $S_0(f)$ when $f$ is an $M$-refinable function. We show that for any $M$-refinable function $f$, there exists a local dual of $f$ in $S_N(f)$ for some $N\ge 0$, and that any function in $S_0(f)$ is poly-scale refinable.
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Additional Information
  • Qiyu Sun
  • Affiliation: Department of Mathematics, University of Central Florida, Orlando, Florida 32816
  • Email: qsun@mail.ucf.edu
  • Received by editor(s): December 17, 2002
  • Received by editor(s) in revised form: December 8, 2003
  • Published electronically: October 14, 2004
  • Additional Notes: Partial results of this paper were announced in the 2002 Fall Southeastern Section Meeting of AMS, Orlando, November 9–10, 2002
  • Communicated by: David R. Larson
  • © Copyright 2004 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 133 (2005), 1175-1184
  • MSC (2000): Primary 42C40, 41A65
  • DOI: https://doi.org/10.1090/S0002-9939-04-07622-1
  • MathSciNet review: 2117220