Gunter Fleischer and Bernd Hofmann 1996 Inverse Problems 12 419 doi:10.1088/0266-5611/12/4/006
Gunter Fleischer and Bernd Hofmann
Show affiliationsAs 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.
65T50 Discrete and fast Fourier transforms
Issue 4 (August 1996)
Received 4 March 1996
Gunter Fleischer and Bernd Hofmann 1996 Inverse Problems 12 419
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