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

Nonnegative Scaling Vectors on the Interval

1
 and
2,*
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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Abstract

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 3.0).

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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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