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Solving singular convolution equations using the inverse Fast Fourier Transform

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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.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Eletrical Engineering, Czech Technical University in Prague, Technická 2, 166 27, Prague 6, Czech Republic

    Eduard Krajník

  2. Instituto de Matemática Pura y Aplicada, Universidad Politécnica de Valencia, C/ Vera, s/n., 46022, Valencia, Spain

    Vincente Montesinos

  3. Department of Math. Physics and Engineering, Mount Royal University, 4825 Mount Royal Gate SW, Calgary, Alberta, Canada

    Peter Zizler

  4. Institute of Mathematics of the Czech Academy of Sciences of the Czech Republic, Žitná 25, 115 67, Praha 1, Czech Republic

    Václav Zizler

Authors
  1. Eduard Krajník
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  2. Vincente Montesinos
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  3. Peter Zizler
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  4. Václav Zizler
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Corresponding author

Correspondence to Eduard Krajník.

Additional information

The second author was supported in part by Proyecto MTM2008-03211, Ministerio de Ciencia e Innovación, by a grant BEST 2010-134 of the Generalitat Valenciana, and by a grant from the Universidad Politécnica de Valencia, PAID 2009, Spain. The fourth author was supported by a grant AVOZ 101 905 03 and IAA 100190901 (Czech Republic).

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Krajník, E., Montesinos, V., Zizler, P. et al. Solving singular convolution equations using the inverse Fast Fourier Transform. Appl Math 57, 543–550 (2012). https://doi.org/10.1007/s10492-012-0032-9

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  • DOI: https://doi.org/10.1007/s10492-012-0032-9

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