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Operators and Equations: Discrete and Continuous

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Abstract

We consider discrete pseudo-differential equations with elliptic symbols and the corresponding discrete boundary-value problems in special canonical domains of multidimensional spaces. The solvability of such equations and boundary-value problems in discrete analogs of Sobolev–Slobodetsky spaces is examined.

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References

  1. S. Bochner andW. T. Martin, Several Complex Variables, Princeton Univ. Press, Princeton (1948).

  2. G. I. Eskin, Boundary-Value Problems for Elliptic Pseudodifferential Equations [in Russian], Nauka, Moscow (1973).

    Google Scholar 

  3. L. S. Frank, “Spaces of grid functions,” Mat. Sb., 86, No. 2, 187–233 (1971).

    MathSciNet  Google Scholar 

  4. L. Hörmander, The Analysis of Linear Partial Differential Operators, Springer-Verlag, Berlin etc. (1985).

  5. S. Rempel and B.-W. Schulze, Index Theory of Elliptic Boundary Problems, Akademie-Verlag, Berlin (1982).

    MATH  Google Scholar 

  6. V. S. Ryaben’ky, Method of Difference Potentials for Some Problems of Continuum Mechanics [in Russian], Nauka, Moscow (1987).

    Google Scholar 

  7. A. A. Samarsky, Theory of Difference Schemes [in Russian], Nauka, Moscow (1971).

    Google Scholar 

  8. M. E. Taylor, Pseudodifferential Operators, Princeton Univ. Press, Princeton, New Jersey (1981).

    Google Scholar 

  9. F. Treves, Introduction to Pseudodifferential and Fourier Integral Operators, Plenum Press, New York–London (1982).

    MATH  Google Scholar 

  10. V. B. Vasilyev, Wave Factorization of Elliptic Symbols: Theory and Applications. Introduction to the Theory of Boundary-Value Problems in Nonsmooth Domains, Kluwer Academic, Dordrecht–Boston–London (2000).

  11. V. B. Vasilyev, Multipliers of Fourier Integrals, Pseudo-Differential Equations, Wave Factorization, and Boundary-Value Problems [in Russian], URSS, Moscow (2010).

    Google Scholar 

  12. V. B. Vasilyev, “Discreteness, periodicity, holomorphy, and factorization,” in: Integral Methods in Science and Engineering. Vol. 1. Theoretical Technique (C. Constanda, M. Dalla Riva, P. D. Lamberti, and P. Musolino, eds.), Birkhäuser (2017), pp. 315–324.

  13. V. B. Vasilyev, “The periodic Cauchy kernel, the periodic Bochner kernel, and discrete pseudodifferential operators,” AIP Conf. Proc., 1863, 140014 (2017).

    Article  Google Scholar 

  14. V. B. Vasilyev, “On discrete boundary-value problems,” AIP Conf. Proc., 1880, 050010 (2017).

    Article  Google Scholar 

  15. V. B. Vasilyev, “Discrete operators in canonical domains,” WSEAS Trans. Math., 16, 197–201 (2017).

    Google Scholar 

  16. V. S. Vladimirov, Methods of the Theory of Functions of Several Complex Variables [in Russian], Nauka, Moscow (1964).

    Google Scholar 

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Authors and Affiliations

  1. Belgorod State National Research University, Belgorod, Russia

    V. B. Vasilyev

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  1. V. B. Vasilyev
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Correspondence to V. B. Vasilyev.

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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 160, Proceedings of the International Conference on Mathematical Modelling in Applied Sciences ICMMAS’17, Saint Petersburg, July 24–28, 2017, 2019.

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Vasilyev, V.B. Operators and Equations: Discrete and Continuous. J Math Sci 257, 17–26 (2021). https://doi.org/10.1007/s10958-021-05465-5

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  • DOI: https://doi.org/10.1007/s10958-021-05465-5

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