A Galerkin-wavelet method for a singular convolution equation on the real line (Q5939759)
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scientific article; zbMATH DE number 1626695
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A Galerkin-wavelet method for a singular convolution equation on the real line |
scientific article; zbMATH DE number 1626695 |
Statements
A Galerkin-wavelet method for a singular convolution equation on the real line (English)
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30 July 2001
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Galerkin method
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Meyer-type wavelets
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singular convolution equations
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error estimation
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The author proposes a Galerkin method based on Meyer-type wavelets (the ``raised-cosine wavelets'') for solving singular convolution equations of the form NEWLINE\[NEWLINE\int^\infty_{-\infty}(H(t- s)+ |t-s|^{-\alpha}) f(s) ds= g(t),\quad t\in\mathbb{R}\quad (0<\alpha< 1),NEWLINE\]NEWLINE where \(H\) lies in the Sobolev space \(H^\beta(\mathbb{R})\), with \(\beta\geq 2\). The analysis focuses on the questions of well-posedness, solvability, and \((L^2\)-) error estimation; there are no numerical examples.
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