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On inversion rates for the autoconvolution equation

Gunter Fleischer and Bernd Hofmann

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As a continuation of a previous paper by one of the authors, this paper presents new results concerning the ill-posedness character of the nonlinear autoconvolution equation when the solution x is a quadratically integrable real function with support in [0,1] and the complete (noisy) data function y can be observed. We discuss quasisolutions restricted to specific (relatively) compact subsets and the chances and limitations of Fourier transform techniques for analysing the autoconvolution problem. Provided that we have uniform minorant and majorant functions for the moduli of Fourier transforms in Q, explicit inversion rates for the autoconvolution equation are derived. A numerical case study illustrates the theoretical results.


PACS

02.30.Uu Integral transforms

02.30.Ik Integrable systems

02.30.Zz Inverse problems

02.60.Ed Interpolation; curve fitting

MSC

65T50 Discrete and fast Fourier transforms

65F22 Ill-posedness, regularization

47J05 Equations involving nonlinear operators (general)

Subjects

Mathematical physics

Computational physics

Dates

Issue 4 (August 1996)

Received 4 March 1996



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