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Local dual and poly-scale refinability

Author: Qiyu Sun
Journal: Proc. Amer. Math. Soc. 133 (2005), 1175-1184
MSC (2000): Primary 42C40, 41A65
Published electronically: October 14, 2004
MathSciNet review: 2117220
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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

Keywords: Local dual, linear independent shifts, refinability, poly-scale refinability
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
Article copyright: © Copyright 2004 American Mathematical Society

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