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.
Kopsch, Anne: On the Construction of Wavelets and Multiwavelets for General Dilation Matrices. : Philipps-Universität Marburg 2023-11-27. DOI: https://doi.org/10.17192/z2023.0672.
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