Vanishing moments for scaling vectors

David K. Ruch

International Journal of Mathematics and Mathematical Sciences, 2004, vol. 2004, 1-12

Abstract:

One advantage of scaling vectors over a single scaling function is the compatibility of symmetry and orthogonality. This paper investigates the relationship between symmetry, vanishing moments, orthogonality, and support length for a scaling vector Φ . Some general results on scaling vectors and vanishing moments are developed, as well as some necessary conditions for the symbol entries of a scaling vector with both symmetry and orthogonality. If orthogonal scaling vector Φ has some kind of symmetry and a given number of vanishing moments, we can characterize the type of symmetry for Φ , give some information about the form of the symbol P ( z ) , and place some bounds on the support of each ϕ i . We then construct an L 2 ( ℠) orthogonal, symmetric scaling vector with one vanishing moment having minimal support.

Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:973921

DOI: 10.1155/S0161171204308215

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