Local dual and poly-scale refinability

Sun, Qiyu

doi:10.1090/S0002-9939-04-07622-1

Local dual and poly-scale refinability
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by Qiyu Sun

Proc. Amer. Math. Soc. 133 (2005), 1175-1184

DOI: https://doi.org/10.1090/S0002-9939-04-07622-1

Published electronically: October 14, 2004

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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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