this article is devoted to study of the autoconvolution equations and generalized mittag-leffler functions. these types of equations are given in terms of the laplace transform convolution of a function with itself. we state new classes of the autoconvolution equations of the first kind and show that the generalized mittag-leffler functions are solutions of these types of equations. in view of ...

This article is devoted to study of the autoconvolution equations and generalized Mittag-Leffler functions. These types of equations are given in terms of the Laplace transform convolution of a function with itself. We state new classes of the autoconvolution equations of the first kind and show that the generalized Mittag-Leffler functions are solutions of these types of equations. In view of ...

Abstract. This paper considers the inverse problem of recovering a nonnegative function from its autoconvolution. We propose an algorithm that solves the problem by minimizing Csiszár’s I-divergence between the observed autoconvolution and an estimated autoconvolution. We call it a deautoconvolution algorithm. Various properties of the algorithm are discussed and proven. The effectiveness of th...

Standard methods for regularizing ill-posed nonlinear equations rely on derivatives of the nonlinear forward mapping. Thereby stronger structural properties of the concrete problem are neglected and the derived algorithms only show mediocre efficiency. We concentrate on nonlinear mappings with quadratic structure and develop a derivative-free regularization method that allows us to apply classi...

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We report femtosecond optical signal processing by using second-order spectral holography. Enhanced secondorder diffraction from a thermoplastic plate makes possible new signal-processing operations not possible with first-order holography. Experiments resulting in output waveforms equal to the autoconvolution function of the input waveform are described, and the possibility of optical signals ...

We pose the problem of approximating optimally a given nonnegative signal with scalar autoconvolution signal. The I-divergence is chosen as optimality criterion being well suited to incorporate nonnegativity constraints. After proving existence an optimal approximation, we derive iterative descent algorithm alternating minimization type find minimizer. based on lifting technique developed by Cs...