Geodesic
Solving singular convolution equations using the inverse fast Fourier transform
Applications of Mathematics, Tome 57 (2012) no. 5, pp. 543-550.

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The inverse Fast Fourier Transform is a common procedure to solve a convolution equation provided the transfer function has no zeros on the unit circle. In our paper we generalize this method to the case of a singular convolution equation and prove that if the transfer function is a trigonometric polynomial with simple zeros on the unit circle, then this method can be extended.
DOI : 10.1007/s10492-012-0032-9
Classification : 42A85, 65R10, 65T50
Keywords: singular convolution equations; fast Fourier transform; tempered distribution; polynomial transfer functions; simple zeros 
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     title = {Solving singular convolution equations using the inverse fast {Fourier} transform},
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Krajník, Eduard; Montesinos, Vincente; Zizler, Peter; Zizler, Václav. Solving singular convolution equations using the inverse fast Fourier transform. Applications of Mathematics, Tome 57 (2012) no. 5, pp. 543-550. doi : 10.1007/s10492-012-0032-9. http://geodesic.mathdoc.fr/articles/10.1007/s10492-012-0032-9/

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