On the Construction of Wavelets and Multiwavelets for General Dilation Matrices

On the Construction of Wavelets and Multiwavelets for General Dilation Matrices

This thesis is concerned with the construction of (pre-)wavelets and (pre-)multiwavelets. In particular, we identify minimal requirements such that a construction is still possible. To this end, we weaken the assumptions made in the definition of the multiresolution analysis. Based on this generaliz...

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Bibliografische gegevens
Hoofdauteur: Kopsch, Anne
Andere auteurs: Dahlke, Stephan (Prof. Dr.) (Thesis begeleider)
Formaat: Dissertation
Taal:Engels
Gepubliceerd in: Philipps-Universität Marburg 2023
Onderwerpen:
Exponential box splines
Wavelet
Shift-invariante Räume
Allgemeine Skalierungsmatrix
General dilation matrix
Shift-invariant spaces
Orthogonale Projektion
Orthogonal projection
Exponentielle Box Splines
Multiwavelet
Mathematik
Mathematics
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Samenvatting:This thesis is concerned with the construction of (pre-)wavelets and (pre-)multiwavelets. In particular, we identify minimal requirements such that a construction is still possible. To this end, we weaken the assumptions made in the definition of the multiresolution analysis. Based on this generalized multiresolution analysis, we develop construction procedures for compactly supported (pre-)wavelets and for compactly supported (pre-)multiwavelets. These construction procedures involve general dilation matrices which allow us to reduce the number of mother wavelets to a minimum. To illustrate the theory developed in this work, we choose exponential box splines as generators for the generalized multiresolution analysis and construct compactly supported (pre-)wavelets and (pre-)multiwavelets.
Fysieke beschrijving:168 Seiten
DOI:10.17192/z2023.0672

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