Multiresolution analysis by the solution of second-kind integral equations (Q2765951)
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scientific article; zbMATH DE number 1695214
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Multiresolution analysis by the solution of second-kind integral equations |
scientific article; zbMATH DE number 1695214 |
Statements
16 June 2002
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Fourier transform
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wavelets
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multiresolution analysis
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Riesz basis
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linear integral equations
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Multiresolution analysis by the solution of second-kind integral equations (English)
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The authors show that if supp \(\widehat{h}(x) = [-\pi,\pi]\), \(\psi(x)\) is a nonzero solution of NEWLINE\[NEWLINE u(x) = \lambda \int_{r} h(2x-y) u(y) dy, NEWLINE\]NEWLINE and \(V_j\) denotes the closure of the linear span of \(\{\psi(2^j x-k)\); \(k \in Z\}\), then \(\{V_j\); \(j \in Z \}\) is a multiresolution analysis and \(\{\psi(x-k)\); \(k \in Z\}\) is a Riesz basis of \(V_0\).
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