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On inversion rates for the autoconvolution equation. (English) Zbl 0862.45007

The authors discuss the ill-posedness of the autoconvolution equation \(x*x=y\) when the solution \(x\) is a quadratically integrable nonnegative real function with support in \([0,1]\) and the complete data information on \(y\) are available, that is, \(y\) is defined on \([0,2]\). Using the Fourier transform technique the explicit inversion rates for the autoconvolution are derived. A numerical case study illustrates the abstract results.
Reviewer: V.Moroz (Minsk)

MSC:

45G10 Other nonlinear integral equations
65R20 Numerical methods for integral equations

Citations:

Zbl 0804.45003
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