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A New Method of Constructions of Non-Tensor Product Wavelets

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Abstract

In this paper, we give a new method of constructions of non-tensor product wavelets. We start from the one-dimensional scaling functions to directly construct the two-dimensional non-tensor product wavelets. The wavelets constructed by us possess very simple, explicit representations and high regularity, and various symmetry (i.e., axial symmetry, central symmetry, and cyclic symmetry). Using this method, we construct various non-tensor product wavelets and show that there exists a sequence of non-tensor product wavelets with high regularity which tends to the tensor product Shannon wavelet in the L 2-norm.

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Authors and Affiliations

  1. Dept. of Math., Univ. of California, Davis, California, 95616, USA

    Zhihua Zhang

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  1. Zhihua Zhang
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Correspondence to Zhihua Zhang.

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Zhang, Z. A New Method of Constructions of Non-Tensor Product Wavelets. Acta Appl Math 111, 153–169 (2010). https://doi.org/10.1007/s10440-009-9537-y

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  • DOI: https://doi.org/10.1007/s10440-009-9537-y

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