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Scaling Functions on R2 for Dilations with Determinant ±2
Rutgers University.
2010 (English)In: Applied and Computational Harmonic Analysis, ISSN 1063-5203, E-ISSN 1096-603X, Vol. 29, no 1, p. 49-62Article in journal (Refereed) Published
Abstract [en]

This paper gives necessary and sufficient conditions for a doubly periodic function p(ξ ), ξ ∈ R2, to be the squared modulus of a lowpass filter for a multiresolution analysis of L2(R2) with respect to an expanding matrix A of determinant ±2. By transferring the underlying spaces, R or R2, to a single binary sequence space, we are able to show that, when det(A) = 2, every scaling function on R2 corresponds to one on R, where the dilation is ±2. If det(A)=−2, this is no longer true. In this case, the lowpass filter for the stretched Haar function makes an unexpected appearance.

Place, publisher, year, edition, pages
2010. Vol. 29, no 1, p. 49-62
Identifiers
URN: urn:nbn:se:ltu:diva-3430DOI: 10.1016/j.acha.2009.08.004Local ID: 140fed47-c126-4b1b-81cf-ebf49b70bb9aOAI: oai:DiVA.org:ltu-3430DiVA, id: diva2:976288
Note
Upprättat; 2010; 20130619 (adajon)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2017-11-24Bibliographically approved

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Jonsson, Adam

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