Wavelet Sets with and without Groups and Multiresolution Analysis

In this dissertation we study a special kind of wavelets, the so-called minimally supported frequency wavelets and the associated wavelet sets. Most of the examples of wavelet sets are for dilation sets which are groups. In this work we construct wavelet sets for which the dilation set, D, is of the...

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Main Author:	Dobrescu, Mihaela
Other Authors:	John Wefel
Format:	Others
Language:	en
Published:	LSU 2005
Subjects:	Mathematics
Online Access:	http://etd.lsu.edu/docs/available/etd-07142005-231924/

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spelling	ndltd-LSU-oai-etd.lsu.edu-etd-07142005-2319242013-01-07T22:50:09Z Wavelet Sets with and without Groups and Multiresolution Analysis Dobrescu, Mihaela Mathematics In this dissertation we study a special kind of wavelets, the so-called minimally supported frequency wavelets and the associated wavelet sets. Most of the examples of wavelet sets are for dilation sets which are groups. In this work we construct wavelet sets for which the dilation set, D, is of the form D=MN, where the product is direct, and so D is not necessarily group. In the second part of this dissertation we construct multiwavelets associated with MRA's and we generalize the rotations in the dilation sets to Coxeter groups. John Wefel Raymond Fabec Jimmie Lawson Frank Neubrander Gestur Olafsson Robert Perlis LSU 2005-07-15 text application/pdf http://etd.lsu.edu/docs/available/etd-07142005-231924/ http://etd.lsu.edu/docs/available/etd-07142005-231924/ en unrestricted I hereby certify that, if appropriate, I have obtained and attached herein a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to LSU or its agents the non-exclusive license to archive and make accessible, under the conditions specified below and in appropriate University policies, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report.
collection	NDLTD
language	en
format	Others
sources	NDLTD
topic	Mathematics
spellingShingle	Mathematics Dobrescu, Mihaela Wavelet Sets with and without Groups and Multiresolution Analysis
description	In this dissertation we study a special kind of wavelets, the so-called minimally supported frequency wavelets and the associated wavelet sets. Most of the examples of wavelet sets are for dilation sets which are groups. In this work we construct wavelet sets for which the dilation set, D, is of the form D=MN, where the product is direct, and so D is not necessarily group. In the second part of this dissertation we construct multiwavelets associated with MRA's and we generalize the rotations in the dilation sets to Coxeter groups.
author2	John Wefel
author_facet	John Wefel Dobrescu, Mihaela
author	Dobrescu, Mihaela
author_sort	Dobrescu, Mihaela
title	Wavelet Sets with and without Groups and Multiresolution Analysis
title_short	Wavelet Sets with and without Groups and Multiresolution Analysis
title_full	Wavelet Sets with and without Groups and Multiresolution Analysis
title_fullStr	Wavelet Sets with and without Groups and Multiresolution Analysis
title_full_unstemmed	Wavelet Sets with and without Groups and Multiresolution Analysis
title_sort	wavelet sets with and without groups and multiresolution analysis
publisher	LSU
publishDate	2005
url	http://etd.lsu.edu/docs/available/etd-07142005-231924/
work_keys_str_mv	AT dobrescumihaela waveletsetswithandwithoutgroupsandmultiresolutionanalysis
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Wavelet Sets with and without Groups and Multiresolution Analysis

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