A regularization procedure for the auto-correlation equation (Q2769913)
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scientific article; zbMATH DE number 1702171
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A regularization procedure for the auto-correlation equation |
scientific article; zbMATH DE number 1702171 |
Statements
A regularization procedure for the auto-correlation equation (English)
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29 September 2002
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auto-correlation equation
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regularization procedure
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quadratic integral equation of the first kind
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regularized equation of the second kind
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stability estimate
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Fourier transform
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convergence
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The paper is devoted to the study of the autocorrelation equation and its regularization by means of Lavrent'ev regularization procedure in \(L^2\). The solution of this quadratic integral equation of the first kind and of the regularized equation of the second kind are obtained by reduction to a boundary value problem for the Fourier transform of the solution. The convergence of the approximate solution to the exact one is proved. A stability estimate for the error is also derived.
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