Givi Khuskivadze

(28.03.1932 – 5.12.2011)

 


Bibliographical  Data:

1950  –

Graduated with honour (gold medal) Tbilisi 8th Secondary School

1955 –

Graduated with honor Faculty of Mechanics and Mathematics of Tbilisi State University

1955 – 1958

Post-graduate student of Tbilisi State University

1963 –

Ph.D  in Mathematics

1967 –

Certificate of Senior Researcher

1970 –

Certificate of Docent 

1999 –

 Dr. Sci. (Phys. & Math.), Tbilisi State University

1958 – 1964

Junior researcher at A. Razmadze Mathematical Institute of Georgian Academy of Sciences

1964 – 1989

Senior researcher at A. Razmadze Mathematical Institute of Georgian Academy of Sciences

1989 – 2006

Leading researcher at A. Razmadze Mathematical Institute of Georgian Academy of Sciences

2006 – 2011

Senior researcher at L.E.P.L. A. Razmadze Mathematical Institute (since 2010 at A. Razmadze Mathematical Institute of Tbilisi State University)

   

The Sphere of Scientific Investigations:

Boundary properties of analytic functions (including conformal mappings). Conjugate functions, the Cauchy type integral, singular Cauchy operator, fractional integrals. Boundary value problems of the theory of analytic and harmonic functions.

 

List of Main Publications

1.             Khuskivadze, G. A. On $A$-integrals of Cauchy type. (Russian) Soobšč. Akad. Nauk Gruzin. SSR 27 1961 663-670. 

2.             Khuskivadze, G. A. Conjugate functions and Cauchy's singular integrals. (Russian) Dokl. Akad. Nauk SSSR 140 1961 1270-1273. 

3.             Khuskivadze, G. A. On conjugate functions and integrals of Cauchy type. (Russian) Soobšč. Akad. Nauk Gruzin. SSR 32 1963 257-263. 

4.             Khuskivadze, G. A. Conjugate functions and integrals of Cauchy type. (Russian)Akad. Nauk Gruzin. SSR Trudy Tbiliss. Mat. Inst. Razmadze 31 1966 5-54.

5.             Khuskivadze, G. A. Cauchy-Stieltjes type integrals. (Russian) Sakharth. SSR Mecn. Akad. Math. Inst. Šrom. 34 1968 160-169. 

6.             Khuskivadze, G. A. Conjugate functions and singular Cauchy-Stieltjes integrals. (Russian) Sakharth. SSR Mecn. Akad. Math. Inst. Šrom. 38 1970 73-84.

7.             Khuskivadze, G. A. The boundedness of a singular operator with Cauchy kernel. (Russian) Collection of articles on the theory of functions, 4. Sakharth. SSR Mecn. Akad. Math. Inst. Šrom. 42 (1972), 95-103. (loose errata). 

8.             Khuskivadze, G. A. Cauchy type integrals. (Russian) Proceedings of the Symposium on Continuum Mechanics and Related Problems of Analysis (Tbilisi, 1971), Vol. 1 (Russian), pp. 233-240. Izdat. "Mecniereba'', Tbilisi, 1973.

9.             Khuskivadze, G. A. The Cauchy singular operator, and the integral of Cauchy type. (Russian) Sakharth. SSR Mecn. Akad. Moambe 79 (1975), no. 1, 33-35.

10.         Khuskivadze, G. A. The singular Cauchy integral, and the integral of Cauchy type. (Russian) Collection of articles on the theory of functions, Vol. 7. Sakharth. SSR Mecn. Akad. Math. Inst. Šrom. 53 (1976), 73-86. 

11.         Paatashvili, V. A.; Khuskivadze, G. A. A singular Cauchy operator on a countable set of concentric circles. (Russian) Trudy Tbiliss. Mat. Inst. Razmadze Akad. Nauk Gruzin. SSR 69 (1982), 80-92. 

12.         Paatashvili, V. A.; Khuskivadze, G. A. Boundedness of a singular Cauchy operator in Lebesgue spaces in the case of nonsmooth contours. (Russian) Trudy Tbiliss. Mat. Inst. Razmadze Akad. Nauk Gruzin. SSR 69 (1982), 93-107.

13.         Paatashvili, V. A., Khuskivadze, G. A. A derivative of a conformal mapping. (Russian) Soobshch. Akad. Nauk Gruzin. SSR 127 (1987), no. 3, 473-475.

14.         Paatashvili, V. A., Khuskivadze, G. A. An application of the linear conjugation problem to the study of the properties of a conformal mapping. (Russian) Trudy Tbiliss. Mat. Inst. Razmadze Akad. Nauk Gruzin. SSR 88 (1989), 27-40.

15.         Paatashvili V., Khuskivadze G. Riemann-Hilbert problem indomains with nonsmooth boundaries. Reports of Enlarged Session of the Seminar of I. Vekua Inst. Appl. Math. 5 (1990), no. 1, 153-156.

16.         Paatashvili V., Khuskivadze G. On the Dirichlet problem for harmonic functions in domains with piecewise smooth boundary. Reports of Enlarged Session of the Seminar of I. Vekua Inst. Appl. Math. 7 (1992), no. 1, ???.

17.         Paatashvili, V. A., Khuskivadze, G. A. The Riemann-Hilbert problem in domains with nonsmooth boundaries. (Russian) Proc. A. Razmadze Math. Inst.106 (1993), 105-122. 

18.         Khuskivadze, G., Paatashvili, V. On the boundedness of Cauchy singular operator from the space $L\sb p$ to $L\sb q,\ p>q\geq 1$. This paper also appears in Georgian Math. J. 1 (1994), no. 4, 395–403. Proc. Georgian Acad. Sci. Math. 1 (1993), no. 4, 443-452. 

19.         Paatashvili, V. A.; Khuskivadze, G. A. On the inclusion of the Cauchy type integrals into the Smirnov's classes. Proc. A. Razmadze Math. Inst. 114 (1997), 71-79. 

20.         Paatashvili, V. A.; Khuskivadze, G. A. On conformal mapping of simply connected domains with a piecewise smooth boundary. Proc. A. Razmadze Math. Inst. 114 (1997), 81-88. 

21.         Paatashvili, V., Khuskivadze, G. On the continuity of the Cauchy operator from the space $L\sb p(\Gamma)$ to $L\sb q(\Gamma)$ for $p>q\geq 1$. Proc. A. Razmadze Math. Inst. 114 (1997), 124-125. 

22.         Khuskivadze, G. Application of an extension of the Lebesgue integral to the investigation of a boundary value problem of linear conjugation. Proc. A. Razmadze Math. Inst. 117 (1998), 71-78. 

23.         Khuskivadze, G. On the derivative of a conformally mapping function. Proc. A. Razmadze Math. Inst. 118 (1998), 53-64. 

24.         Khuskivadze, G.; Paatashvili, V. On the conformal mapping of a circle onto a domain with an arbitrary piecewise smooth boundary. Proc. A. Razmadze Math. Inst. 116 (1998), 123-132.

25.         Khuskivadze, G.; Kokilashvili, V.; Paatashvili, V. Boundary value problems for analytic and harmonic functions in domains with nonsmooth boundaries. Applications to conformal mappings. Mem. Differential Equations Math. Phys. 14 (1998), 195 pp.

26.         Khuskivadze G., Paatashvili, V. On Conformal Mapping of the Domain with a Piecewise Smooth Curve on the Same Domain. Reports of enlarged session of the seminar of I. Vekua Institute of Appl. Math. 13 (1998), No. 1, 20-22.

27.         Khuskivadze, G.; Paatashvili, V. On the boundedness of the Cauchy singular operator. Proc. A. Razmadze Math. Inst. 124 (2000), 107-114.

28.         Khuskivadze, G.; Paatashvili, V. On a representation of the derivative of a conformal mapping. Georgian Math. J. 8 (2001), no. 3, 513-520. 

29.         Khuskivadze, G.; Paatashvili, V. Zaremba's problem in one class of harmonic functions. Proc. A. Razmadze Math. Inst. 132 (2003), 143-147. 

30.         Khuskivadze, G.; Paatashvili, V. On Zaremba's boundary value problem for harmonic functions of Smirnov classes. Mem. Differential Equations Math. Phys. 32 (2004), 29-58. 

31.         Khuskivadze, G.; Paatashvili, V. On a property of harmonic functions from the Smirnov class. Mem. Differential Equations Math. Phys. 33 (2004), 87-94.

32.         Khuskivadze, G.; Paatashvili, V. On the conformal mapping of simply connected domains with non-Jordan boundaries. Proc. A. Razmadze Math. Inst.136 (2004), 85-90. 

33.         Khuskivadze, G.; Paatashvili, V. On the Dirichlet problem for harmonic functions of Smirnov classes in doubly-connected domains. Proc. A. Razmadze Math. Inst. 136 (2004), 141-144. 

34.         Khuskivadze, G.; Paatashvili, V. Zaremba's problem for harmonic functions from the Smirnov's weighted classes in domains with piecewise Lyapunov boundaries. Proc. A. Razmadze Math. Inst. 142 (2006), 129-133. 

35.         Khuskivadze, G.; Paatashvili, V. Zaremba's problem in Smirnov class of harmonic functions in domains with piecewise-Lyapunov boundaries. Proc. A. Razmadze Math. Inst. 143 (2007), 79-94. 

36.         Khuskivadze, G.; Paatashvili, V. On the Dirichlet problem for harmonic functions from Smirnov classes in doubly-connected domains. Proc. A. Razmadze Math. Inst. 144 (2007), 41-60. 

37.         Khuskivadze, G.; Paatashvili, V. The Dirichlet problem for harmonic functions of Smirnov classes in doubly-connected domains with arbitrary piecewise smooth boundaries. Proc. A. Razmadze Math. Inst. 146 (2008), 67-78.

38.         Khuskivadze, G,. On fractional integrals on the plane curves of finite length.Georgian Math. J. 15 (2008), no. 2, 327-332. 

39.         Khuskivadze, G.; Paatashvili, V. Zaremba's boundary value problem in the Smirnov class of harmonic functions in domains with piecewise-smooth boundaries. Mem. Differential Equations Math. Phys. 51 (2010), 73-91.

40.         Khuskivadze, G.; Kokilashvili, V.; Paatashvili, V. The Dirichlet problem for variable exponent Smirnov class harmonic functions in doubly-connected domains. Mem. Differential Equations Math. Phys. 52 (2011), 131-156.

 

 

Note dedicated to G. Khuskivadze

1.         Bantsuri, R.; Kekelidze, N.; Kiguradze, I.; Kokilashvili, V.; Paatashvili, V.;Oziashvili, T. On the occasion of Givi Khuskivadze's 80th birthday anniversary. Mem. Differential Equations Math. Phys. 56 (2012), 1-7.