Abstract
We describe the so-called method of virtual components for tight wavelet framelets to increase their approximation order and vanishing moments in the multivariate setting. Two examples of the virtual components for tight wavelet frames based on bivariate box splines on three or four direction mesh are given. As a byproduct, a new construction of tight wavelet frames based on box splines under the quincunx dilation matrix is presented.
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Communicated by Stephan Dahlke.
The research is supported by the National Science Foundation under grant #DMS 0713807.
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Lai, MJ., Petukhov, A. The Method of Virtual Components in the Multivariate Setting. J Fourier Anal Appl 16, 471–494 (2010). https://doi.org/10.1007/s00041-009-9108-7
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DOI: https://doi.org/10.1007/s00041-009-9108-7