arXiv subjects
Publications and source records attributed to A. K. Bakhtin.
Paper is devoted to extremal problems in geometric function theory of complex variables associated with estimates of functionals defined on the systems of non-overlapping domains. In particular, we strengthen some known result in this subject.
We study one extremal problem on the product of power of generalized inner radii of non-overlapping domains in $\mathbb{C}^{n}$.
In this paper we consider quite general problem on non-overlapping domains with free poles on radial systems. The main theorem of this work generalizes the previously known results for problems of this type.
The paper proposes a vector generalization of the basic concepts of the theory of complex variable: the concept of modulus and argument of complex number. The author introduces some generalizations of the notion of holomorphic functions and mappings to the case of infinite-dimensional complex spaces. This approach allows us to generalize several well-known results of geometric function theory to the case of infinite-dimensional complex spaces. In particular, the author summarizes a number of known theorems on the theory of functions of class S on infinite-dimensional complex space.