Compactly supported wavelets and representations of the Cuntz relations

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dc.creatorBratteli, Ola
dc.creatorEvans, David E.
dc.creatorJorgensen, Palle E. T.
dc.date1999-12-15
dc.date.accessioned2026-07-07T05:32:19Z
dc.date.available2026-07-07T05:32:19Z
dc.descriptionWe study the harmonic analysis of the quadrature mirror filters coming from multiresolution wavelet analysis of compactly supported wavelets. It is known that those of these wavelets that come from third order polynomials are parametrized by the circle, and we compute that the corresponding filters generate irreducible mutually disjoint representations of of the Cuntz algebra $ O_{2} $ except at two points on the circle. One of the two exceptional points corresponds to the Haar wavelet and the other is the unique point on the circle where the father function defines a tight frame which is not an orthonormal basis. At these two points the representation decomposes into two and three mutually disjoint irreducible representations, respectively, and the two representations at the Haar point are each unitarily equivalent to one of the three representations at the other singular point.
dc.descriptionAMS-LaTeX; 29 pages, 6 figures incorporating 23 EPS diagrams and 1 LaTeX picture
dc.identifierhttps://arxiv.org/abs/math/9912129
dc.identifierhttp://arxiv.org/abs/math/9912129
dc.identifierApplied and Computational Harmonic Analysis 8 (2000), 166--196.
dc.identifierdoi:10.1006/acha.2000.0283
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/79617
dc.subjectFunctional Analysis
dc.subject46L60, 47D25, 42A16, 43A65 (Primary) 46L45, 42A65, 41A15 (Secondary)
dc.titleCompactly supported wavelets and representations of the Cuntz relations
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