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Siberian Mathematical Journal

, Volume 60, Issue 4, pp 585–591 | Cite as

Noethericity and Index of a Characteristic Bisingular Integral Operator with Shifts

  • S. V. EfimovEmail author
Article
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Abstract

We consider a characteristic bisingular operator with rather arbitrary shifts that decompose into one-dimensional components. We reduce the problem about the Noethericity and index to that about an operator without shifts. The results obtained are straightforwardly applicable to the two-dimensional boundary-value problem with shifts which is a natural generalization of the Haseman and Carleman problems.

Keywords

Noethericity index bisingular operator shift 

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References

  1. 1.
    Efimov S. V., “Noethericity and index of characteristic bisingular operator with shift,” Vladikavkazsk. Mat. Zh., vol. 16, no. 2, 46–48 (2014).MathSciNetzbMATHGoogle Scholar
  2. 2.
    Sazonov L. I., “A bisingular equation with translation in the space Lp,” Math. Notes, vol. 13, no. 3, 235–239 (1973).CrossRefzbMATHGoogle Scholar
  3. 3.
    Pilidi V. S. and Stefanidi E. N., “On an algebra of bisingular operators with shift,” Rostov-on-Don, 1981. 26 pp. Submitted to VINITI, no. 3036.Google Scholar
  4. 4.
    Pilidi V. S. and Stefanidi E. N., “On an algebra of bisingular operators with shift,” Izv. Vyssh. Uchebn. Zaved. Mat., no. 9, 80–81 (1981).Google Scholar
  5. 5.
    Efimov S. V., “Bisingular operators with irreducible involutive shift,” Russian Math. (Iz. VUZ), no. 2, 29–36 (1992).Google Scholar
  6. 6.
    Efimov S. V., “On effectively verifiable conditions of the Noethericity of some bisingular operators with shift,” in: Integro-Differential Operators and Its Applications, Don State Technical University, Rostov-on-Don, 1997, no. 2, 75–78.Google Scholar
  7. 7.
    Efimov S. V., “Index of some bisingular integral operators with shift,” in: Integro-Differential Operators and Its Applications, Don State Technical University, Rostov-on-Don, 1998, no. 3, 61–66.Google Scholar
  8. 8.
    Efimov S. V., “Index of some bisingular operators with irreducible shift,” in: Integro-Differential Operators and Its Applications, Don State Technical University, Rostov-on-Don, 2001, no. 5, 88–94.Google Scholar
  9. 9.
    Efimov S. V., “Calculation of the index of some bisingular operators with irreducible involutive shift,” Izv. Vyssh. Uchebn. Zaved. Severo-Kavkaz. Reg. Estestv. Nauk, no. 9, 7–14 (2004).Google Scholar
  10. 10.
    Efimov S. V., “On the index of some bisingular integral operators with shift,” Vestnik Don State Technical University, vol. 4, no. 3, 290–295 (2004).Google Scholar
  11. 11.
    Efimov S. V., “Calculation of the index of some bisingular operators with shift by the homotopy method,” Vestnik Don State Technical University, vol. 10, no. 1, 22–27 (2010).Google Scholar
  12. 12.
    Pilidi V. S., “On a bisingular equation in the space Lp,” in: Mat. Issled., Shtiintsa, Kishinev, 1972, vol. 7, no. 3, 167–175.MathSciNetGoogle Scholar
  13. 13.
    Pilidi V. S., “Index computation for a bisingular operator,” Funct. Anal. Appl., vol. 7, no. 4, 337–338 (1973).CrossRefzbMATHGoogle Scholar
  14. 14.
    Gokhberg I. Ts. and Krupnik N. Ya., An Introduction to the Theory of One-Dimensional Singular Integral Operators [Russian], Shtiintsa, Kishinev (1973).Google Scholar
  15. 15.
    Litvinchuk G. S., Boundary Value Problems and Singular Integral Equations with Shift [Russian], Nauka, Moscow (1977).zbMATHGoogle Scholar
  16. 16.
    Simonenko I. B., “Some general questions in the theory of the Riemann boundary problem,” Math. USSR-Izv., vol. 2, no. 5, 1091–1099 (1968).CrossRefzbMATHGoogle Scholar
  17. 17.
    Lavrentiev M. A. and Shabat B. V., Methods of the Theory of Functions of Complex Variables [Russian], Nauka, Moscow (1987).Google Scholar
  18. 18.
    Goluzin G. M., Geometric Theory of Functions of a Complex Variable, Amer. Math. Soc., Providence (1969).CrossRefzbMATHGoogle Scholar

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© Pleiades Publishing, Inc. 2019

Authors and Affiliations

  1. 1.North Caucasus Branch of Moscow Technical University of Communications and InformaticsRostov-on-DonRussia

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