Preview

Chebyshevskii Sbornik

Advanced search

Carleman’s formula for the matrix domains of Siegel

https://doi.org/10.22405/2226-8383-2022-23-4-126-135

Abstract

The domain of Siegel first type is not a bounded domain, but Carleman’s formulas for it play an important role in the further presentation. In this paper, the Carleman formula for the Siegel domain is found.

About the Authors

Uktam Sodikovich Rakhmonov
Tashkent State Technical University
Uzbekistan

associate professor



Zokirbek Kadamovich Matyakubov
Khorezm Academy of Mamun
Uzbekistan

postgraduate student



References

1. T.Carleman, Les fonctions quasi analytiques, Paris: Gauthier-Villars (1926), pp. 3–6.

2. G. M. Golusin, W. J. Krylow, Verallgemeinerung einer Formel von Carleman und ihre

3. Anwendung zur analytischen Fortsetzung, Mat. Sb., 40:2 (1933), 144–149.

4. Hua Luogeng, Harmonic analysis of functions of several complex variables, in classical domains,

5. Moscow, IL, 1963 (in Russian).

6. A.M.Kytmanov, T.N.Nikitina, Analogs of Carleman’s formula for classical domains, Math.

7. Notes, 45:3 (1989), 243–248.

8. A.M.Kytmanov, T.N.Nikitina, Multidimensional Carleman formulas in Siegel domain, Soviet

9. Math. (Iz. VUZ), 34:3 (1990), 50–56.

10. S.Kosbergenov, On the Carleman formula for a matrix ball, Russian Math. (Iz. VUZ), 43:1

11. (1999), 72–75.

12. G.Khudayberganov, U.S.Rakhmonov, Z.Q.Matyakubov, Integral formulas for some matrix

13. domains, Contemporary Mathematics, AMS, Volume 662, pp. 89-95.(2016).

14. G.Khudayberganov, U.S.Rakhmonov, The Bergman and Cauchy-Szego kernels for matrix ball

15. of the second type, Journal of Siberian Federal University. Mathematics and Physics 7:3, pp.

16. -310.(2014).

17. G.Khudayberganov, B.P.Otemuratov, U.S.Rakhmonov, Boundary Morera theorem for the

18. matrix ball of the third type, Journal of Siberian Federal University. Mathematics and Physics,

19. :1, 40-45.(2018).

20. G.Khudayberganov, U.S.Rakhmonov, Carleman Formula for Matrix Ball of the Third Type,

21. Algebra, Complex Analysis, and Pluripotential Theory. USUZCAMP 2017. Springer Proceedings

22. in Mathematics and Statistics vol. 264, pp. 101-108, Springer, Cham.(2017).

23. U. S. Rakhmonov, J. Sh. Abdullayev, On volumes of matrix ball of third type and generalized

24. Lie balls, Вестн. Удмуртск. ун-та. Матем. Мех. Компьют. науки, 29:4 (2019), 548–557

25. G. Khudayberganov, J. Abdullayev, Relationship between the Kernels Bergman and Cauchy-

26. Szeg˝o in the domains 𝜏+ (𝑛 − 1) and ℜ𝑛𝐼

27. 𝑉 , Journal of Siberian Federal University. Mathematics

28. & Physics, 13:5, 559-567(2020).

29. G.Khudayberganov, A.M.Khalknazarov, J.Sh.Abdullayev, Laplace and Hua Luogeng operators,

30. Russian Math. (Iz. VUZ), 64:3 (2020), 66–71.

31. L. A. Aizenberg, Carleman Formulas in complex analysis, Novosibirsk, Nauka, 1990 (in

32. Russian).

33. P. Kusis, Introduction to the theory of spaces 𝐻𝑝 . М.: Мир. 1984. 368 с.

34. G. Khudayberganov, A. M. Kytmanov, B. A. Shaimkulov, Analysis in matrix domains, Monograph.

35. Krasnoyarsk, Siberian Federal University, 2017 (in Russian).

36. I. I. Privalov, Boundary properties of analytic functions, M.: Gostekhizdat, 1950. – 338 с.

37. Jonibek Sh. Abdullayev. An analogue of Bremermann’s theorem on finding the Bergman kernel

38. for the Cartesian product of the classical domains ℜ𝐼 (𝑚, 𝑘) and ℜ𝐼𝐼 (𝑛), Bul. Acad. Stiinte

39. Repub. Mold. Mat., 2020, no. 3, 88–96.

40. G. Khudayberganov, J. Sh. Abdullayev. The boundary Morera theorem for domain 𝜏+ (𝑛 − 1),

41. Ufimsk. Mat. Zh., 13:3 (2021), pp. 196–210.

42. K. Rakhimov, Sh. Shopulatov. A mean value criterion for plurisubharmonic functions, Complex

43. Variables and Elliptic Equations, (2021) DOI:10.1080/17476933.2021.1954623.

44. G. Khudayberganov, J. Sh. Abdullayev. Holomorphic continuation into a matrix ball of

45. functions defined on a piece of its skeleton, Vestnik Udmurtskogo Universiteta. Matematika.

46. Mekhanika. Komp’yuternye Nauki, 2021, vol. 31, issue 2, pp. 296–310.

47. J. Sh. Abdullayev. Estimates the Bergman kernel for classical domains E. Cartan’s, Chebyshevskii

48. sbornik, 2021, vol. 22, no. 3, pp. 21–32.

49. Uktam S. Rakhmonov, Jonibek Sh. Abdullayev, (2022), On properties of the second type matrix

50. ball 𝐵(2)

51. 𝑚,𝑛 from space C𝑛[𝑚 × 𝑚], J. Sib. Fed. Univ. Math. Phys., 15:3, pp. 329–342.


Review

For citations:


Rakhmonov U.S., Matyakubov Z.K. Carleman’s formula for the matrix domains of Siegel. Chebyshevskii Sbornik. 2022;23(4):126-135. (In Russ.) https://doi.org/10.22405/2226-8383-2022-23-4-126-135

Views: 301


Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.


ISSN 2226-8383 (Print)