Fleischer, Gunter; Hofmann, Bernd On inversion rates for the autoconvolution equation. (English) Zbl 0862.45007 Inverse Probl. 12, No. 4, 419-435 (1996). 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) Cited in 12 Documents MSC: 45G10 Other nonlinear integral equations 65R20 Numerical methods for integral equations Keywords:ill-posed problems; autoconvolution equation; Fourier transform technique; inversion rates; numerical case study Citations:Zbl 0804.45003 PDFBibTeX XMLCite \textit{G. Fleischer} and \textit{B. Hofmann}, Inverse Probl. 12, No. 4, 419--435 (1996; Zbl 0862.45007) Full Text: DOI