List of Main Publications of Omar Dzagnidze

Mnographs

  1. Some new results on the continuity and differentiability of functions of several real variables. Proc. A. Razmadze Math. Inst. 134 (2004), 1-138. (http://www.rmi.acnet.ge/proceedings/volumes/134.htm)

Papers

  1. Representation of measurable functions of two variables by double series. (Russian) Soobshch. Akad. Nauk Gruzin. SSR 34 (1964), No. 2, 277-282.
  2. On universal double series. (Russian) Soobshch. Akad. Nauk Gruzin. SSR 34 (1964), No. 3, 525-528.
  3. The universal harmonic function in the space En. (Russian) Soobshch. Akad. Nauk Gruzin. SSR 55 (1969), No. 2, 41-44.
  4. The boundary behavior of functions defined in a ball. (Russian) Soobshch. Akad. Nauk Gruzin. SSR 55 (1969), No. 2, 281-284.
  5. A certain subclass of nowhere dense sets. (Russian) Soobshch. Akad. Nauk Gruzin. SSR 60 (1970), No. 2, 289-291.
  6. *Certain boundary properties of functions that are harmonic in a ball. (Russian) Dokl. Akad. Nauk SSSR 198 (1971), No. 5, 1005-1006.
  7. To the boundary behaviour of functions, harmonic in a sphere. Tezisy dokl. vsesoyuzn. conf. v TFKP. Kharkov, FTI AN Ukrain. SSR 4(1971), 29-30.
  8. Certain boundary properties of functions harmonic in a ball. (Russian) Trudy Tbiliss. Mat. Inst. Razmadze 42 (1972), 65-77.
  9. Geometric definition of functions of the Fedorov-Smirnov class. (Russian) Soobshch. Akad. Nauk Gruzin. SSR 95 (1979), No. 2, 281-283.
  10. M. Riesz's LF-inequality for the Fedorov-Smirnov class of functions. (Russian) Soobshch. Akad. Nauk Gruzin. SSR 95 (1979), No. 3, 545-548.
  11. The inequalities of M. Riesz, A. Kolmogorov and A. Zygmund for functions of the Fedorov-Smirnov class. (Russian) Trudy Tbiliss. Mat. Inst. Razmadze 65 (1980), 51-64.
  12. Plessner and Meier theorems for harmonic functions of the Fedorov-Smirnov class. (Russian) Trudy Tbiliss. Mat. Inst. Razmadze 65 (1980), 65-72.
  13. L2-approximation by Hartogs-Laurent and Hartogs-Fourier polynomials. (Russian) Trudy Tbiliss. Mat. Inst. Razmadze 65 (1980), 73-84.
  14. Some integral inequalities. (Russian) Trudy Tbiliss. Mat. Inst. Razmadze 69 (1982), 38-50.
  15. Holomorphy and membership of functions in the Fedorov-Smirnov class. (Russian) Soobshch. Akad. Nauk Gruzin. SSR 108 (1982), No. 2, 257-259.
  16. Partial derivatives with boundary behavior and variation of the Poisson integral. (Russian) Trudy Tbiliss. Mat. Inst. Razmadze  76 (1985), 18-39.
  17. Partial derivatives of the Poisson integral and their boundary properties. (Russian) Reports of the extended sessions of a seminar of the I. N. Vekua Institute of Applied Mathematics, Vol. I, No. 2 (Russian) (Tbilisi, 1985), 75-78, 181, Tbilis. Gos. Univ., Tbilisi, 1985.
  18. On the plane variation and gradient of a function harmonic in a ball. (Russian) Soobshch. Akad. Nauk Gruzin. SSR 120 (1985), No. 3, 473-475.
  19. Formulas for a mixed derivative of the Poisson integral and its boundary properties. (Russian) Soobshch. Akad. Nauk Gruzin. SSR 120 (1985), No. 2, 241-244.
  20. Hartogs-Fourier series. (Russian) Theory of functions and approximations, Part 2 (Russian) (Saratov, 1984), 97-98, Saratov. Gos. Univ., Saratov, 1986.
  21. Representation of a pair of functions by derivatives of the Poisson integral. (Russian) Soobshch. Akad. Nauk Gruzin. SSR 122 (1986), No. 1, 21-23.
  22. A mixed derivative of the Poisson integral. (Russian) Trudy Tbiliss. Mat. Inst. Razmadze  86 (1987), 24-39.
  23. Boundary values of the derivatives of the Poisson integral, and the representation of functions. (Russian) Soobshch. Akad. Nauk Gruzin. SSR 128 (1987), No. 2, 269-271.
  24. Convergence of a Hartogs-Fourier series. (Russian) Soobshch. Akad. Nauk Gruzin. SSR 129 (1988), No. 2, 257-260.
  25. A-Summability of the differentiated Fourier-Laplace series. (Russian) Soobshch. Akad. Nauk Gruzii 140 (1990), No. 3, 489-492.
  26. Generalizations of Fatou and Luzin theorems for derivatives of the Poisson integral on a sphere. (Russian) Soobshch. Akad. Nauk Gruzin. SSR 139 (1990), No. 1, 29-32.
  27. Angular limits at the poles of a sphere of the derivatives of the Poisson integral. (Russian) Trudy Tbiliss. Mat. Inst. Razmadze  98 (1991), 99-111.
  28. Boundary values of the derivatives of the Poisson integral for a ball and the representation of functions of two variables. (Russian) Trudy Tbiliss. Mat. Inst. Razmadze  98 (1991), 52-98.
  29. Angular limits of additional terms in the derivative of the Poisson spherical integral. Proc. A. Razmadze Math. Inst. 101 (1992), 27-37.
  30. On the mixed partial derivatives of Poisson integral. In: “Integral operators and boundary properties of functions. Fourier series. Research reports of Razmadze Math. Inst., Tbilisi, Georgia”. Nova Science Publishers, Inc. New York, 1992, 29-50.
  31. Differentiability of the indefinite double Lebesgue integral. (Russian) Soobshch. Akad. Nauk Gruzii 147 (1993), No. 1, 22-25.
  32. Boundary properties of second order derivatives of the Poisson spherical integral. Proc. A. Razmadze Math. Inst. 102 (1993), 9-27.
  33. Some criteria for the differentiability of functions of two variables. (Russian) Soobshch. Akad. Nauk Gruzii 148 (1993), No. 1, 9-12.
  34. On the differentiability of functions of two variables and of indefinite double integrals. Proc. A. Razmadze Math. Inst. 106 (1993), 7-48.
  35. Lebesgue points and segments for functions of two variables. (Russian) Soobshch. Akad. Nauk Gruzii 151 (1995), No. 3, 369-372.
  36. Total differential of the indefinite Lebesgue integral. Proc. A. Razmadze Math. Inst. 114 (1997), 27-34.
  37. Associated integrals, functions, series and radial derivative of the Poisson spherical integral. Proc. A. Razmadze Math. Inst. 114 (1997), 107-111.
  38. *Allied integrals, functions and series for the unit sphere. Georgian Math. J. 5 (1998), No. 3, 213-232.
  39. For Fourier analysis on the sphere. Bull. Georgian Acad. Sci. 158 (1998), No. 3, 357-360.
  40. *Separately continuous functions in new sense are continuous. Real Anal. Exchange 24 (1998/1999), No. 2, 695-702.
  41. *A radial derivative with boundary values of the spherical Poisson integral. Georgian Math. J. 6 (1999), No. 1, 19-32.
  42. A necessary and sufficient condition for differentiability functions of several variables. Proc. A. Razmadze Math. Inst. 123 (2000), 23-29.
  43. On the limit and continuity of functions of several variables. Proc. A. Razmadze Math. Inst. 124 (2000), 23-29.
  44. The continuity and the limit in the wide. Their connection with the continuity and limit. Proc. A. Razmadze Math. Inst. 128 (2002), 37-46.
  45. Unilateral in various senses: the limit, continuity, partial derivative and the differential for functions of two variables. Proc. A. Razmadze Math. Inst. 129 (2002), 1-15.
  46. On one analogue of Lebesgue theorem on the differentiation of indefinite integral for functions of several variables (with G. Oniani). Proc. A. Razmadze Math. Inst. 132 (2003), 139-140 and 133 (2003), 1-5.
  47. Relation between the continuity of a function gradient and the finiteness of its strong gradient. Proc. A. Razmadze Math. Inst. 135 (2004), 57-59.
  48. Necessary and sufficient conditions for Cn-differentiability and the Hartogs main theorem. Proc. A. Razmadze Math. Inst. 138 (2005), 103-105.
  49. A note to the Lebesgue  and de la Vallee Poussin’s theorems on derivation of an integral. Tatra Mountains Mathematical Publications 35 (2007), 107-113.
  50. A criterion of joint C-differentiability and a new proof of Hartogs’ main theorem. J. Appl. Anal. 13 (2007), No. 1, 13-17.
  51. *The smoothness of functions of two variables and double trigonometric series. Real Anal. Exchange 34 (2008/2009), No. 2, 451-470.
  52. On the derivability and representations of quaternion functions. Rep. Enlarged Sess. Semin. I. Vekua Inst. App. Math. 23 (2009), 25-30.
  53. The smoothness of functions of two variables and double trigonometric series. Semin. I. Vekua Inst. Appl. Math. Rep. 35 (2009), 21-25.
  54. Integration of double Fourier trigonometric series. Proc. A. Razmadze Math. Inst. 155 (2011), 110-112.
  55. On the differentiability of quaternion functions. Tbil. Math. J. 5 (2012), 1-15.
  56. Representing summable functions of two variables by double exponential Fourier series. Proc. A. Razmadze Math. Inst. 162 (2013), 127-129.
  57. Convergence of double trigonometric series obtained by termwise integration. Rep. Enlarged Sess. Semin. I. Vekua Appl. Math. 28 (2014), 24-27.
  58. On the differentiability of real, complex and quaternion functions. Bull. TICMI 18 (2014), no. 1, 93-109.
  59. On the behaviour of series, obtained by termwise integration of double trigonometric series. Proc. A. Razmadze Math. Inst. 166 (2014), 31-48.
  60. ქართული მათემატიკური ტერმინოლოგიის ჩამოყალიბების ისტორიისთვის. ტერმინოლოგიის საკითხები, I, თბილისი, 2014, 187-197.
  61. For history of formation of the Georgian mathematical, technical and natural sciences terminology. Rep. Enlarged Sess. Semin. I. Vekua Appl. Math. 28 (2014), 28-31.
  62. *Necessary and sufficient conditions for the $\Bbb{H}$-differentiability of quaternion functions. Georgian Math. J. 22 (2015), no. 2, 215-218.
  63. $\Bbb C^2$-differentiability of quaternion functions and their representation by integrals and series. Proc. A. Razmadze Math. Inst. 167 (2015), 19-27.
  64. თოფთან დაკავშირებული ზოგიერთი ტერმინის დაზუსტებისთვის. ტერმინოლოგიის საკითხები, II, თბილისი, 2016, 141-151.
  65. ფუნქციურ მწკრივთა თეორიის ერთი ტერმინის შესახებ. ტერმინოლოგიის საკითხები, II, თბილისი, 2016, 152-153.
  66. *Symmetric convergence of double series whose coefficients are the quotients of divisions of complex Fourier coefficients by their indexes. Georgian Math. J. 24 (2017), no. 4
  67.  One-dimensional Fourier series of a function of many variables. Trans. A. Razmadze Math. Inst. 171 (2017), 167-170.