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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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| Formato: | Dissertation |
| Idioma: | inglês |
| Publicado em: |
Philipps-Universität Marburg
2023
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| Assuntos: | |
| Acesso em linha: | Texto integral em PDF |
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| Resumo: | 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. |
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| Descrição Física: | 168 Seiten |
| DOI: | 10.17192/z2023.0672 |