analytic functions

Siegеl disks and basins of attraction for families of analytic functions

Authors: Gumenuk P. A.

Let be a hyperbolic domain, , let ∆ be a Stolz angle at with respect to the unit disk D, and W a domain containing the point λ0 . Consider an analytic family ; consisting of analytic functions in the domain U with the following expansion , λ ∈ W, for small z. Let be the maximal domain A ⊂ U, such that 0 ∈ A and f l (A) ⊂ A, or the set {0} if there exist no such domains. We prove, that if a sequence converges to λ0 and , then the sequence of the domains converges to S as to the kernel.

About New Approach to Solution of Riemann’s Boundary Value Problem with Condition on the Half-line in Case of Infinite Index

Authors: Salimov R. B.

To solve a homogeneous Riemann boundary value problem with infinite index and condition on the half-line we propose a new approach based on the reduction of the considered problem to the corresponding task with the condition on the real axis and finite index.

The Solution of the Homogeneous Riemann Boundary Value Problem with a Countable Set of Points of Discontinuity of the First Kind its Coefficient

Authors: Salimov R. B.

We consider the Riemann homogeneous boundary value problem with a countable set of points of discontinuity of the first kind in the case, when it is required to find two functions, analytic, respectively, in the upper and lower half-plane, for a given linear boundary condition on the real axis, connecting the boundary values of the unknown functions.