Department of Complex Analysis

The Department of Complex Analysis (known as The Department of theory of functions of complex variable until 2002) was organized in 1964. The first Head of the Department was S. N. Mergelyan, and first members of the Department were A. G. Vitushkin, A. A. Gonchar, and A. F. Leont'ev. From 1972 to 2002, the Head of the Department was A. A. Gonchar.

2002, Corresponding Member of RAS E. M. Chirka has headed the Department.

The traditional research area in the Department is the theory of approximation in a complex domain. For first years of activity, works of members of the Department gave further elaborating to classical results of M. V. Keldysh, M. A. Lavrent'ev, and S. N. Mergelyan. The study of qualitative questions of the possibility of uniform approximation by rational functions on compacts in the complex plane was completed with the fundamental Vitushkin theorem. There are widely known the works of A. F. Leont'ev devoted to exponent polynomials and Dirichlet series, and the results of A. A. Gonchar on the best approximations of analytic functions by rational functions.

Since the beginning of the 1970s, the main efforts of A. A. Gonchar and his followers are concentrated on the development of constructive methods of rational approximations of analytic functions, their theoretical foundation and applications. Results obtained by members of the Department cover a wide range of problems connected with theory of convergence of Padé approximations and more general interpolations processes, problems of evaluating asymptotics in theory of orthogonal polynomials, classical problems on a speed of rational approximations of analytical functions, and other problems of complex analysis (A. A. Gonchar, E. A. Rakhmanov, S. P. Suetin, and V. I. Buslaev).

Among important results obtained at the Department are results on the theory of real manifolds in a complex space, on the theory of analytical sets, and on boundary properties of holomorphic functions of several complex variables (A. G. Vitushkin, E. M. Chirka, N. G. Kruzhilin, S. Yu. Orevkov, and S. Yu. Nemirovskii).

In different years, the contributions of S. N. Mergelyan (1952), A. G. Vitushkin (1967), A. F. Leont'ev (1989) and A. A. Gochar (1999) were awarded State Prizes; A. A. Gonchar is a prize-winner of Demidov Prize (1999); S. Yu. Nemirovskii is a prize-winner of the European Mathematical Society Prize for Young Scientists (2000).

A large number of the invited speakers on International Mathematical Congresses consist of the members of the Department:

A. G. Vitushkin (Moscow, 1966; Vancouver, 1974)

A. A. Gonchar (Moscow, 1966; Berkeley, 1986)

S. N. Mergelyan (Nice, 1970)

N. G. Kruzhilin (Berkeley, 1986)

S. Yu. Nemirovskii (Barcelone, 2000)