Refinable subspaces of a refinable space

Hardin, Douglas; Hogan, Thomas

doi:10.1090/S0002-9939-99-05297-1

Refinable subspaces of a refinable space
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by Douglas P. Hardin and Thomas A. Hogan

Proc. Amer. Math. Soc. 128 (2000), 1941-1950

DOI: https://doi.org/10.1090/S0002-9939-99-05297-1

Published electronically: October 29, 1999

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Abstract:

Local refinable finitely generated shift-invariant spaces play a significant role in many areas of approximation theory and geometric design. In this paper we present a new approach to the construction of such spaces. We begin with a refinable function $\psi :\mathbb {R}\to \mathbb {R}^{m}$ which is supported on $[0,1]$. We are interested in spaces generated by a function $\phi :\mathbb {R}\to \mathbb {R}^{n}$ built from the shifts of $\psi$.

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