Potential Theory, Theory of Analytic and Subharmonic Functions, Approximation Theory.
Main publications:
A uniqueness theorem for meromorphic functions. - Izv. Akad. Nauk Armjan. SSR.
Ser. Mat. 15 (1980), no. 2, 110–126.
On the radii of exceptional disks in lower estimates of the modulus of functions of
bounded type. - Uspekhi Mat. Nauk 36 (1981), no. 6(222), 233–234.
Decrease on a sequence of points of a function holomorphic on a half plane. - Sibirsk. Mat. Zh. 24 (1983), no. 2, 180–192.
The estimations outside exceptional sets and uniqueness theorems for $\delta$-subharmonic functions. Thesis. Moscow, 1983, 130 p.
On the algorithm of Diliberto and Straus for approximating bivariate functions by sums $g(x)+h(y)$. - Sibirsk. Mat. Zh. 28 (1987), no. 5, 223–224. The complete version is deposited at VINITI, no. 2505-B, 1986, 16 p.
Exceptional sets in asymptotic estimates of subharmonic functions. - Sibirsk. Mat. Zh. 29 (1988), no. 6, 185–196.
Measure and capacity of exceptional sets arising in estimations of $\delta$-subharmonic functions. - Potential Theory. Proc. Intern. Conf. on Potential Theory, Nagoya, 1990.
Ed. M. Kishi et al. Walter de Gruyter Publ., 1992, 171–177.
On the comparison of Hausdorff measure and capacity. - Algebra i Analis 3 (1991), no. 6, 174–189. = St. Petersburg Math. J. 3 (1992), no. 6, 1367–1381.
On a sum of values on the sequence of points for functions from some classes. - Izvestiya Vuzov. Mat. 1992, no. 1, 89–97.
Metric characteristics of exceptional sets arising in estimations of subharmonic functions. - Mat. Sbornik 185 (1994), no. 10, 145–160.
(with M. Essen) On exceptional sets for superharmonic functions in a halfspace: an inverse problem. - Math. Scandinavica 76 (1995), 273–288.
On a conjecture of L. D. Ivanov. - In: Linear and Complex Analysis Problem Book 3, Vol. 2. Lect. Notes in Math. 1574. Springer, 1994, 152–153.
On an approximation by polynomials with small coefficients. - Mat. Zametki (Math. Notes) 57 (1995), no. 1, 150–153.
(with M. Essén) Harmonic majorization of $|x_1|$ in subsets of $\mathbf R^n$, $n\ge 2$ - Ann. Acad. Sci. Fenn. Math. 21 (1996), no. 1, 223–240.
Estimates of potentials and $\delta$-subharmonic functions outside exceptional sets. - Izv. Ross. Akad. Nauk, Matem. 61 (1997), no. 6, 181–218.
Hausdorff measure and capacity associated with the Cauchy potentials. - Math. Zametki (Math. Notes) 63 (1998), no. 6, 923–934.
Metric properties of exceptional sets. - Complex Analysis and Differential Equations. Proceedings of the Marcus Wallenberg Symposium in Honor of Matts Essen Held in Uppsala, Sweden, June 15–18, 1997. Uppsala: Uppsala Univ., 1999.
Metric characteristics of exceptional sets and uniqueness theorems in function theory. Doctorate thesis. Moscow, 1999, 192 p.
(with M. Essén) Uniqueness theorems for analytic and subharmonic functions. - Algebra i Analiz 14 (2002), no. 6, 1–88. = St. Petersburg Math. J. 14 (2003), no. 6, 889–952.
(with P. Thomas) Equivalence of summatory conditions along sequences for bounded holomorphic functions. - Complex Var. Theory Appl. 49 (2004), no. 7–9, 595–611.
Capacities of generalized Cantor sets. - In: Selected Topics in Complex Analysis. The S. Ya. Khavinson Memorial Volume. Operator Theory: Adv. And Appl., Vol. 158. Birkhauser, 2005, pp. 131–139.
(with J. M. Anderson) Estimates for the Cauchy transform of point masses (the logarithmic derivative of polynomials). - Dokl. Akad. Nauk, 401 (2005), no. 5, 583–586. = Doklady Mathematics, 71 (2005), no. 2, 241–244.
(with J. M. Anderson) Cauchy transforms of point masses: the logarithmic derivative of polynomials. - Ann. Math. 163 (2006), 1057–1076.
