On homogeneous Riemann boundary value problem on the arcs of infinite length (Q1311161)

The author considers a Riemann boundary value problem \[ \varphi^ + (t)=G(t) \varphi^ -(t),\;t \in \Gamma \backslash \{a_ 1,a_ 2\}, \] on a non-smooth and non-rectifiable curve \(\Gamma\) with the following conditions at the end-points: \(\varphi(z)=O (| z-a_ j |^{- \gamma})\), \(\gamma<1\), \(j=1,2\). He announces some new results about solvability of this problem in terms which are connected with the increase of the function \[ k_ \Gamma(z)=(2 \pi i)^{-1} \ln ((z-a_ 2)/(z-a_ 1))=O(| z-a_ j |^{-\lambda} ),\;\lambda >0. \] The author considers a locally rectifiable curve and coefficients which are Taylor differentiable at the points \(a_ 1\), \(a_ 2\) (or differentiable in the ``real'' sense).