From filters to wavelets via direct limits

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dc.creatorLarsen, Nadia S.
dc.creatorRaeburn, Iain
dc.date2006-02-21
dc.date.accessioned2026-07-07T07:03:38Z
dc.date.available2026-07-07T07:03:38Z
dc.descriptionWe present a new proof of a theorem of Mallat which describes a construction of wavelets starting from a quadrature mirror filter. Our main innovation is to show how the scaling function associated to the filter can be used to identify a certain direct limit of Hilbert spaces with $L^2(\R)$ in such a way that one can immediately identify the wavelet basis. Our arguments also use a pair of isometries introduced by Bratteli and Jorgensen, and exploit the geometry inherent in the Cuntz relations satisfied by these isometries.
dc.description6 pages, to appear in GPOTS 2005 proceedings
dc.identifierhttps://arxiv.org/abs/math/0602450
dc.identifierhttp://arxiv.org/abs/math/0602450
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/109045
dc.subjectFunctional Analysis
dc.subjectOperator Algebras
dc.subject42C40
dc.titleFrom filters to wavelets via direct limits
dc.typetext

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