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Axioms 2013, 2(3), 371-389; doi:10.3390/axioms2030371

Nonnegative Scaling Vectors on the Interval

1 Department of Mathematical and Computer Sciences, Metropolitan State University of Denver, Denver, CO 80217, USA 2 Department of Mathematics, University of St. Thomas, St. Paul, MN 55105, USA
* Author to whom correspondence should be addressed.
Received: 17 April 2013 / Revised: 28 June 2013 / Accepted: 1 July 2013 / Published: 9 July 2013
(This article belongs to the Special Issue Wavelets and Applications)
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In this paper, we outline a method for constructing nonnegative scaling vectors on the interval. Scaling vectors for the interval have been constructed in [1–3]. The approach here is different in that the we start with an existing scaling vector ϕ that generates a multi-resolution analysis for L2(R) to create a scaling vector for the interval. If desired, the scaling vector can be constructed so that its components are nonnegative. Our construction uses ideas from [4,5] and we give results for scaling vectors satisfying certain support and continuity properties. These results also show that less edge functions are required to build multi-resolution analyses for L2 ([a; b]) than the methods described in [5,6].
Keywords: scaling functions; (compactly supported) scaling vectors scaling functions; (compactly supported) scaling vectors
This is an open access article distributed under the Creative Commons Attribution License (CC BY) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Ruch, D.K.; Van Fleet, P.J. Nonnegative Scaling Vectors on the Interval. Axioms 2013, 2, 371-389.

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