Abstract
This paper presents a brief survey of several recent applications of multilevel techniques, in particular, in connection with the solution of periodic pseudodifferential equations. It is pointed out that these applications naturally lead to certain decompositions of refinable spaces which are induced by a class of linear projectors. Then recent results on the construction of such nonorthogonal wavelets are reviewed and extended to the particular needs of the present context.
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Dahmen, W. Decomposition of refinable spaces and applications to operator equations. Numer Algor 5, 229–245 (1993). https://doi.org/10.1007/BF02210384
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DOI: https://doi.org/10.1007/BF02210384
Keywords
- Stable decompositions
- periodic multiresolution analysis
- pseudodifferential equations
- preconditioning
- decompositions of refinable spaces
- matrix equations