Generalized Multiresolution Analysis: Construction and Measure Theoretic Characterization

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dc.contributor.advisorBenedetto, John J.en_US
dc.contributor.authorRomero, Juan R.en_US
dc.contributor.departmentMathematicsen_US
dc.contributor.publisherDigital Repository at the University of Marylanden_US
dc.contributor.publisherUniversity of Maryland (College Park, Md.)en_US
dc.date.accessioned2005-10-11T10:31:44Z
dc.date.available2005-10-11T10:31:44Z
dc.date.issued2005-08-03en_US
dc.description.abstractIn this dissertation, we first study the theory of frame multiresolution analysis (FMRA) and extend some of the most significant results to d - dimensional Euclidean spaces. A main feature of this theory is the fact that it was successfully applied to narrow band signals; however, the theory does have its limitations. Some orthonormal wavelets may not be obtained by the methods of FMRA. This is because non-MRA orthonormal wavelets have nonconstant dimension functions. This means that the number of scaling functions needed is more than one. The appropiate tools for non-MRA wavelets are the generalized multiresolution analyses (GFMRA, GMRA) theories developed by Manos Papadakis and Lawrence Baggett. At the end, we unify both theories by finding an explicit formula for an important map. Our approach also permits us to give a short and elegant proof of a classical result about a special type of decomposition in shift-invariant space theory.en_US
dc.format.extent364885 bytes
dc.format.mimetypeapplication/pdf
dc.identifier.urihttp://hdl.handle.net/1903/2942
dc.language.isoen_US
dc.subject.pqcontrolledMathematicsen_US
dc.subject.pquncontrolledFrameen_US
dc.subject.pquncontrolledMultiresolutionen_US
dc.subject.pquncontrolledWaveletsen_US
dc.titleGeneralized Multiresolution Analysis: Construction and Measure Theoretic Characterizationen_US
dc.typeDissertationen_US

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