We introduce and study certain distributions generalizing the operation of curvilinear integration for the case where the path of integration is not rectifiable. Then we apply that distributions for solving of boundary value problems of Riemann-Hilbert type in domains with non-rectifiable boundaries.

No abstract

No abstract

No abstract

Let Γ be a closed non-rectifiable Jordan curve on the complex plane C. We consider the socalled jump problem, i.e. the boundary value problem for determination of a holomorphic in C \ Γ function with a given jump on Γ . The main result is a condition of solvability of the problem in terms of a new metric dimension of the curve.