List of Main Publications of Omar Dzagnidze
Mnographs
- 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
- Representation of measurable
functions of two variables by double series. (Russian) Soobshch. Akad. Nauk
Gruzin. SSR 34 (1964), No. 2, 277-282.
- On universal double series.
(Russian) Soobshch. Akad. Nauk Gruzin. SSR 34 (1964), No. 3,
525-528.
- The universal harmonic
function in the space En. (Russian) Soobshch. Akad. Nauk
Gruzin. SSR 55 (1969), No. 2, 41-44.
- The boundary behavior of
functions defined in a ball. (Russian) Soobshch. Akad. Nauk Gruzin. SSR
55 (1969), No. 2, 281-284.
- A certain subclass of
nowhere dense sets. (Russian) Soobshch. Akad. Nauk Gruzin. SSR 60
(1970), No. 2, 289-291.
- *Certain boundary properties
of functions that are harmonic in a ball. (Russian) Dokl. Akad. Nauk SSSR
198 (1971), No. 5, 1005-1006.
- 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.
- Certain boundary properties
of functions harmonic in a ball. (Russian) Trudy Tbiliss. Mat. Inst.
Razmadze 42 (1972), 65-77.
- Geometric definition of
functions of the Fedorov-Smirnov class. (Russian) Soobshch. Akad. Nauk
Gruzin. SSR 95 (1979), No. 2, 281-283.
- M. Riesz's LF-inequality
for the Fedorov-Smirnov class of functions. (Russian) Soobshch. Akad. Nauk
Gruzin. SSR 95 (1979), No. 3, 545-548.
- 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.
- Plessner and Meier theorems
for harmonic functions of the Fedorov-Smirnov class. (Russian) Trudy
Tbiliss. Mat. Inst. Razmadze 65 (1980), 65-72.
- L2-approximation
by Hartogs-Laurent and Hartogs-Fourier polynomials. (Russian) Trudy Tbiliss.
Mat. Inst. Razmadze 65 (1980), 73-84.
- Some integral inequalities.
(Russian) Trudy Tbiliss. Mat. Inst. Razmadze 69 (1982), 38-50.
- Holomorphy and membership of
functions in the Fedorov-Smirnov class. (Russian) Soobshch. Akad. Nauk
Gruzin. SSR 108 (1982), No. 2, 257-259.
- Partial derivatives with
boundary behavior and variation of the Poisson integral. (Russian) Trudy
Tbiliss. Mat. Inst. Razmadze 76 (1985), 18-39.
- 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.
- 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.
- 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.
- Hartogs-Fourier series.
(Russian) Theory of functions and approximations, Part 2 (Russian) (Saratov,
1984), 97-98, Saratov. Gos. Univ., Saratov, 1986.
- Representation of a pair of
functions by derivatives of the Poisson integral. (Russian) Soobshch. Akad.
Nauk Gruzin. SSR 122 (1986), No. 1, 21-23.
- A mixed derivative of the
Poisson integral. (Russian) Trudy Tbiliss. Mat. Inst. Razmadze 86
(1987), 24-39.
- 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.
- Convergence of a Hartogs-Fourier
series. (Russian) Soobshch. Akad. Nauk Gruzin. SSR 129 (1988),
No. 2, 257-260.
- A-Summability of the
differentiated Fourier-Laplace series. (Russian) Soobshch. Akad. Nauk
Gruzii 140 (1990), No. 3, 489-492.
- 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.
- 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.
- 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.
- Angular limits of additional
terms in the derivative of the Poisson spherical integral. Proc. A. Razmadze
Math. Inst. 101 (1992), 27-37.
- 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.
- Differentiability of the
indefinite double Lebesgue integral. (Russian) Soobshch. Akad. Nauk Gruzii
147 (1993), No. 1, 22-25.
- Boundary properties of
second order derivatives of the Poisson spherical integral. Proc. A. Razmadze
Math. Inst. 102 (1993), 9-27.
- Some criteria for the
differentiability of functions of two variables. (Russian) Soobshch. Akad.
Nauk Gruzii 148 (1993), No. 1, 9-12.
- On the differentiability of
functions of two variables and of indefinite double integrals. Proc. A. Razmadze
Math. Inst. 106 (1993), 7-48.
- Lebesgue points and segments
for functions of two variables. (Russian) Soobshch. Akad. Nauk Gruzii
151 (1995), No. 3, 369-372.
- Total differential of the
indefinite Lebesgue integral. Proc. A. Razmadze Math. Inst. 114
(1997), 27-34.
- Associated integrals,
functions, series and radial derivative of the Poisson spherical integral.
Proc. A. Razmadze Math. Inst. 114 (1997), 107-111.
- *Allied integrals, functions
and series for the unit sphere. Georgian Math. J. 5 (1998),
No. 3, 213-232.
- For Fourier analysis on the
sphere. Bull. Georgian Acad. Sci. 158 (1998), No. 3, 357-360.
- *Separately continuous
functions in new sense are continuous. Real Anal. Exchange 24
(1998/1999), No. 2, 695-702.
- *A radial derivative with
boundary values of the spherical Poisson integral. Georgian Math. J.
6 (1999), No. 1, 19-32.
- A necessary and sufficient
condition for differentiability functions of several variables. Proc. A. Razmadze
Math. Inst. 123 (2000), 23-29.
- On the limit and continuity
of functions of several variables. Proc. A. Razmadze Math. Inst. 124
(2000), 23-29.
- The continuity and the limit
in the wide. Their connection with the continuity and limit. Proc. A. Razmadze
Math. Inst. 128 (2002), 37-46.
- 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.
- 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.
- Relation between the
continuity of a function gradient and the finiteness of its strong gradient.
Proc. A. Razmadze Math. Inst. 135 (2004), 57-59.
- Necessary and sufficient
conditions for Cn-differentiability and the Hartogs main theorem.
Proc. A. Razmadze Math. Inst. 138 (2005), 103-105.
- 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.
- A
criterion of joint C-differentiability and a new proof of Hartogs’ main
theorem. J. Appl. Anal. 13 (2007), No. 1, 13-17.
- *The smoothness of functions
of two variables and double trigonometric series. Real Anal. Exchange
34 (2008/2009), No. 2, 451-470.
- On the derivability and representations of quaternion functions. Rep.
Enlarged Sess. Semin. I. Vekua Inst. App. Math. 23 (2009), 25-30.
- The smoothness of functions of two variables and double trigonometric
series. Semin. I. Vekua Inst. Appl. Math. Rep. 35 (2009),
21-25.
- Integration of double Fourier trigonometric series. Proc. A. Razmadze
Math. Inst. 155 (2011), 110-112.
- On the differentiability of quaternion functions. Tbil. Math. J.
5 (2012), 1-15.
- Representing summable functions of two variables by double exponential
Fourier series. Proc. A. Razmadze Math. Inst. 162 (2013),
127-129.
- Convergence of double trigonometric series obtained by termwise
integration. Rep. Enlarged Sess. Semin. I. Vekua Appl. Math. 28
(2014), 24-27.
- On the differentiability of real, complex and quaternion functions.
Bull. TICMI 18 (2014), no. 1, 93-109.
- On the behaviour of series, obtained by termwise integration of double
trigonometric series. Proc. A. Razmadze Math. Inst. 166
(2014), 31-48.
- ქართული მათემატიკური ტერმინოლოგიის ჩამოყალიბების ისტორიისთვის.
ტერმინოლოგიის საკითხები, I, თბილისი, 2014, 187-197.
- 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.
- *Necessary and sufficient conditions for the $\Bbb{H}$-differentiability
of quaternion functions. Georgian Math. J. 22 (2015), no. 2,
215-218.
- $\Bbb C^2$-differentiability of quaternion functions and their
representation by integrals and series. Proc. A. Razmadze Math. Inst.
167 (2015), 19-27.
- თოფთან
დაკავშირებული ზოგიერთი ტერმინის დაზუსტებისთვის. ტერმინოლოგიის საკითხები,
II,
თბილისი, 2016,
141-151.
- ფუნქციურ მწკრივთა თეორიის ერთი ტერმინის შესახებ. ტერმინოლოგიის
საკითხები, II, თბილისი, 2016, 152-153.
- *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
- One-dimensional Fourier series of a function of many variables. Trans. A. Razmadze Math. Inst.
171 (2017), 167-170.