On the new family of wavelets interpolating to the Shannon wavelet (Q2843173)
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scientific article; zbMATH DE number 6197347
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the new family of wavelets interpolating to the Shannon wavelet |
scientific article; zbMATH DE number 6197347 |
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On the new family of wavelets interpolating to the Shannon wavelet (English)
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9 August 2013
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Shannon wavelet
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orthonormal wavelets
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convergence
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It is well-known that the \(B\)-spline functions \(M_n\) converge to the Gauss function. Since those functions are not orthogonal to their integer translates, K. H. Oh and others proved that Battle-Lemarié's father wavelets (orthogonalization of \(B\)-spline functions) converge to Shannon function, as \(n\) goes to infinity. The paper under review defines a new family of orthonormal wavelets with parameter \(n\), and shows that they converge to the Shannon's function in the \(L^p(\mathbb R)\) sense.
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