Homogeneous approximation property for continuous wavelet transforms |
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Authors: | Bei Liu Wenchang Sun |
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Institution: | aDepartment of Mathematics, Nankai University, Tianjin 300071, China;bLPMC, Nankai University, Tianjin 300071, China |
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Abstract: | The homogeneous approximation property (HAP) for frames is useful in practice and has been developed recently. In this paper, we study the HAP for the continuous wavelet transform. We show that every pair of admissible wavelets possesses the HAP in L2 sense, while it is not true in general whenever pointwise convergence is considered. We give necessary and sufficient conditions for the pointwise HAP to hold, which depends on both wavelets and functions to be reconstructed. |
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Keywords: | Admissible Continuous wavelet transform Homogeneous approximation property HAP |
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