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International Conference on Numerical Analysis and Its Applications

NAA 2016: Numerical Analysis and Its Applications pp 706–712Cite as

Discrete Approximations for Multidimensional Singular Integral Operators

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10187))

Abstract

For discrete operator generated by singular kernel of Calderon–Zygmund one introduces a finite dimensional approximation which is a cyclic convolution. Using properties of a discrete Fourier transform and a finite discrete Fourier transform we prove a solvability for approximating equation in corresponding discrete space. For comparison discrete and finite discrete solution we obtain an estimate for a speed of convergence for a certain right-hand side of considered equation.

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References

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Acknowledgments

The work was supported by Russian Foundation for Basic Research and Lipetsk regional government of Russia, project No. 14-41-03595-r-center-a.

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Authors and Affiliations

  1. Department of Mathematical Analysis, National Research Belgorod State University, Studencheskaya 14/1, 308007, Belgorod, Russia

    Alexander Vasilyev & Vladimir Vasilyev

  2. Chair of Pure Mathematics, Lipetsk State Technical University, Moskovskaya 30, 398600, Lipetsk, Russia

    Alexander Vasilyev & Vladimir Vasilyev

Authors
  1. Alexander Vasilyev
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  2. Vladimir Vasilyev
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Corresponding author

Correspondence to Vladimir Vasilyev .

Editor information

Editors and Affiliations

  1. Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Ivan Dimov

  2. Department of Applied Analysis, Eötvös Loránd University, Budapest, Hungary

    István Faragó

  3. Department of Applied Mathematics and Statistics, University of Rousse, Ruse, Bulgaria

    Lubin Vulkov

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Vasilyev, A., Vasilyev, V. (2017). Discrete Approximations for Multidimensional Singular Integral Operators . In: Dimov, I., Faragó, I., Vulkov, L. (eds) Numerical Analysis and Its Applications. NAA 2016. Lecture Notes in Computer Science(), vol 10187. Springer, Cham. https://doi.org/10.1007/978-3-319-57099-0_81

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  • DOI: https://doi.org/10.1007/978-3-319-57099-0_81

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-57098-3

  • Online ISBN: 978-3-319-57099-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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