On the autoconvolution equation and total variation constraints

This paper is concerned with the numerical analysis of the autoconvolution equation x * x = y restricted to the interval [0,1]. We present a discrete constrained least squares approach and prove its convergence in L-P(0, 1), 1 less than or equal to p < infinity, where the regularization is based on a prescribed bound Sor the total variation of admissible solutions. This ap proach includes the case of non-smooth solutions possessing jumps. Moreover , an adaptation to the Sobolev space H-1(0,1) is added. A numerical case st udy concerning the determination of nan-monotone smooth and non-smooth func tions x from the autoconvolution equation with noisy data y completes the p aper.