Nonnegative Scaling Vectors on the Interval
AbstractIn 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].
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Ruch, D.K.; Van Fleet, P.J. Nonnegative Scaling Vectors on the Interval. Axioms 2013, 2, 371-389.
Ruch DK, Van Fleet PJ. Nonnegative Scaling Vectors on the Interval. Axioms. 2013; 2(3):371-389.Chicago/Turabian Style
Ruch, David K.; Van Fleet, Patrick J. 2013. "Nonnegative Scaling Vectors on the Interval." Axioms 2, no. 3: 371-389.