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Continuation of Polyanalytic Functions

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Abstract

We investigate the problem of continuation of an n-analytic function into a domain by the values of its successive derivatives up to the \((n-1)\)th order given on a part of the boundary. For such functions, we also consider the problem of finding the conditions under which the Cauchy type integral becomes the Cauchy integral.

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REFERENCES

  1. Balk M.B. "Polyanalytic functions and their generalizations", Complex analysis. One variable – 1, Itogi Nauki i Tekhniki., Ser. Sovrem. Probl. Mat. Fund. Napr. 85, 187-246 (1991) [in Russian].

    MathSciNet  MATH  Google Scholar 

  2. Begehr H., Kumar A. "Boundary value problems for bipolyanalytic functions", Appl. Anal. 85 (9), 1045-1077 (2006).

    Article  MathSciNet  Google Scholar 

  3. Begehr A.H. "A boundary value problem for Bitsadze equation in the unit disc", J. Contemporary Math. Anal. 42, 177-183 (2007).

    Article  MathSciNet  Google Scholar 

  4. Lavrentiev M.M., Romanov V.G., Shishatskii S.P. Ill-posed Problems of Mathematical Physics (Nauka, Moscow, 1980) [in Russian].

    Google Scholar 

  5. Evgrafov M.A. Analytic Functions (Nauka, Moscow, 1991) [in Russian].

    Google Scholar 

  6. Teodoresku N. La dérivée aréolaire et ses applications à la physique mathématique (Gauthier-Villars, Paris, 1931).

    Google Scholar 

  7. Aizenberg L.A. Carleman Formulas in Complex Anaysis (Nauka, Novosibirsk, 1990) [in Russian].

    Google Scholar 

  8. Muskhelishvili N.I. Singular Integral Equations (Fizmatgiz, Moscow, 1962) [in Russian].

    MATH  Google Scholar 

  9. Fock V.A., Kuni F.M. "On introducing of extinguishing function in dispersion relations", Dokl. Akad. Nauk SSSR 127 (6), 1195-1196 (1959) [in Russian].

    Google Scholar 

  10. Ptrivalov I.I. Boundary properties of analytic functions (Gostekhizdat, Moscow, 1950) [in Russian].

    Google Scholar 

  11. Pokazeev V.V. "Integrals of the Cauchy type for polyanalytic functions", Trudy Sem. Kraev. Zadacham, Kazan University 17, 133-139 (1980) [in Russian].

    MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Samarkand State University, 15 University blv., 140104, Samarkand, Uzbekistan

    T. Ishankulov

  2. Samarkand Branch of Tashkent University of Information Technologies named after Muhammad al-Khwarizmi, 47a Shohruh Mirzo str., 140100, Samarkand, Uzbekistan

    D. Sh. Fozilov

Authors
  1. T. Ishankulov
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  2. D. Sh. Fozilov
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Corresponding authors

Correspondence to T. Ishankulov or D. Sh. Fozilov.

Additional information

Russian Text © The Author(s), 2021, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2021, No. 8, pp. 37–45.

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Ishankulov, T., Fozilov, D.S. Continuation of Polyanalytic Functions. Russ Math. 65, 32–39 (2021). https://doi.org/10.3103/S1066369X21080041

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  • DOI: https://doi.org/10.3103/S1066369X21080041

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