Title page for ETD etd-07142005-231924


Type of Document Dissertation
Author Dobrescu, Mihaela
Author's Email Address dobrescu@math.lsu.edu
URN etd-07142005-231924
Title Wavelet Sets with and without Groups and Multiresolution Analysis
Degree Doctor of Philosophy (Ph.D.)
Department Mathematics
Advisory Committee
Advisor Name Title
Gestur Olafsson Committee Chair
Frank Neubrander Committee Member
Jimmie Lawson Committee Member
Raymond Fabec Committee Member
Robert Perlis Committee Member
John Wefel Dean's Representative
Keywords
  • tilings
  • multiresolution analysis
  • wavelet sets
  • coxeter groups
  • spectral pairs
Date of Defense 2005-07-05
Availability unrestricted
Abstract
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.
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