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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Refinable subspaces of a refinable space


Authors: Douglas P. Hardin and Thomas A. Hogan
Journal: Proc. Amer. Math. Soc. 128 (2000), 1941-1950
MSC (1991): Primary 39A10, 39B62, 42B99, 41A15
Published electronically: October 29, 1999
MathSciNet review: 1662241
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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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Additional Information

Douglas P. Hardin
Affiliation: Department of Mathematics, Vanderbilt University, Nashville, Tennessee 37240
Email: hardin@math.vanderbilt.edu

Thomas A. Hogan
Affiliation: Department of Mathematics, Vanderbilt University, Nashville, Tennessee 37240
Email: hogan@math.vanderbilt.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05297-1
PII: S 0002-9939(99)05297-1
Keywords: Refinability, matrix subdivision, refinable function vector, multiwavelet, shift-invariant, FSI
Received by editor(s): February 4, 1998
Received by editor(s) in revised form: August 5, 1998
Published electronically: October 29, 1999
Additional Notes: This research was partially supported by a grant from the NSF and a grant from the Vanderbilt University Research Council.
Communicated by: David R. Larson
Article copyright: © Copyright 2000 American Mathematical Society