Affine Density in Wavelet Analysis

Kutyniok, Gitta

doi:10.1007/978-3-540-72949-5

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Homogeneous approximation property for continuous wavelet transforms

Liu

Sun

2008

Journal of Approximation Theory

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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 L 2 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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