Construction of Parseval wavelets from redundant filter systems

dc.creatorBaggett, L. W.
dc.creatorJorgensen, P. E. T.
dc.creatorMerrill, K. D.
dc.creatorPacker, J. A.
dc.date2004-05-14
dc.date2005-05-05
dc.date.accessioned2026-07-07T06:21:35Z
dc.date.available2026-07-07T06:21:35Z
dc.descriptionWe consider wavelets in L^2(R^d) which have generalized multiresolutions. This means that the initial resolution subspace V_0 in L^2(R^d) is not singly generated. As a result, the representation of the integer lattice Z^d restricted to V_0 has a nontrivial multiplicity function. We show how the corresponding analysis and synthesis for these wavelets can be understood in terms of unitary-matrix-valued functions on a torus acting on a certain vector bundle. Specifically, we show how the wavelet functions on R^d can be constructed directly from the generalized wavelet filters.
dc.description34 pages, AMS-LaTeX ("amsproc" document class) v2 changes minor typos in Sections 1 and 4, v3 adds a number of references on GMRA theory and wavelet multiplicity analysis; v4 adds material on pages 2, 3, 5 and 10, and two more references
dc.identifierhttps://arxiv.org/abs/math/0405301
dc.identifierhttp://arxiv.org/abs/math/0405301
dc.identifierdoi:10.1063/1.1982768
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/95645
dc.subjectClassical Analysis and ODEs
dc.subjectOperator Algebras
dc.subjectPrimary 54C40, 14E20, 42A65; Secondary 46E25, 20C20
dc.titleConstruction of Parseval wavelets from redundant filter systems
dc.typetext

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