бесконечный индекс

The Solution of the Homogeneous Boundary Value Problem of Riemann with Infinite Index of Logarithmic Order on the Beam by a New Method

Authors: Salimov R. B., Khasanova E. N.

In this paper we consider the homogeneous Riemann boundary value problem with infinite index of logarithmic order and boundary condition on the unlimited ray. This ray goes by the positive real axis and has a vertex. We solve the problem for analytic function with the cut along the ray. The value of the function at any point of the left bank equals the product of the coefficient and the value of the function at the corresponding point of the right bank of the cut. Let the modulus of the coefficient  meet the Holder condition at each point of the ray.

Investigation Riemann – Hilbert Boundary Value Problem with Infinite Index on Circle

Authors: Fatykhov A. K., Shabalin P. L.

We consider the Riemann – Hilbert boundary value problem of analytic function theory with infinite index and the boundary condition on the circumference. The boundary condition coefficients are Holder’s continuous everywhere except one particular point where the coefficients have discontinuity of second kind (power order with the index is less than one). In this formulation the problem with infinite index is considered for the first time.

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.