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 | References | Similar Articles | Additional Information

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 which is supported on . We are interested in spaces generated by a function built from the shifts of .

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

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