E. Krajník, Department of Mathematics, Faculty of Eletrical Engineering, Czech Technical University in Prague, Technická 2, 166 27 Prague 6, Czech Republic, e-mail: firstname.lastname@example.org; V. Montesinos, Instituto de Matemática Pura y Aplicada, Universidad Politécnica de Valencia, C/ Vera, s/n. 46022 Valencia, Spain, e-mail: email@example.com; P. Zizler, Department of Math. Physics and Engineering, Mount Royal University, 4825 Mount Royal Gate SW, Calgary, Alberta, Canada, e-mail: firstname.lastname@example.org; V. Zizler, Institute of Mathematics of the Czech Academy of Sciences of the Czech Republic, Žitná 25, 115 67 Praha 1, Czech Republic, e-mail: email@example.com
Abstract: 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.
Keywords: singular convolution equations, fast Fourier transform, tempered distribution, polynomial transfer functions, simple zeros
Classification (MSC 2010): 42A85
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