APPLICATIONS OF MATHEMATICS, Vol. 57, No. 5, pp. 543-550, 2012

Solving singular convolution equations using the inverse fast Fourier transform

Eduard Krajník, Vincente Montesinos, Peter Zizler, Václav Zizler

E. Krajník, Department of Mathematics, Faculty of Eletrical Engineering, Czech Technical University in Prague, Technická 2, 166 27 Prague 6, Czech Republic, e-mail: krajnik@math.feld.cvut.cz; V. Montesinos, Instituto de Matemática Pura y Aplicada, Universidad Politécnica de Valencia, C/ Vera, s/n. 46022 Valencia, Spain, e-mail: vmontesinos@mat.upv.es; P. Zizler, Department of Math. Physics and Engineering, Mount Royal University, 4825 Mount Royal Gate SW, Calgary, Alberta, Canada, e-mail: pzizler@mtroyal.ca; 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: zizler@math.cas.cz

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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