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Localization of Dual Periodic Scaling and Wavelet Functions

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Abstract

In 1996, we constructed periodic interpolatory scaling functions ϕ j , wavelet functions L j and their dual basis \(\widetilde{\varphi _j }{\text{ and }}\widetilde L_j\) with properties such as symmetry, biorthogonality, any order of smoothness, real-valuedness, explicit expressions and interpolatory. We proved the localization of ϕ j in 1997, and in 1998 with Li proved the localization of L j . In this paper we shall give a detailed proof of the localization for the dual functions \(\widetilde{\varphi _j }{\text{ and }}\widetilde L_j\).

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Authors and Affiliations

  1. Chinese Academy of Sciences, Institute of Mathematics, 100080, Beijing, P.R. China

    Han-Lin Chen

  2. Chinese Academy of Sciences, Institute of Automation, 100080, Beijing, P.R. China

    Si-Long Peng

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  1. Han-Lin Chen
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Chen, HL., Peng, SL. Localization of Dual Periodic Scaling and Wavelet Functions. Advances in Computational Mathematics 19, 195–210 (2003). https://doi.org/10.1023/A:1022882423107

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