Spectral analysis of the Dirac system with a singularity in an interior point

We study the non-selfadjoint Dirac system on the line having an non-integrable regular singularity in an interior point with additional matching conditions at the singular point. Special fundamental systems of solutions are constructed with prescribed analytic and asymptotic properties. Behavior of the corresponding Stockes multipliers is established. These fundamental systems of solutions will be used for studying direct and inverse problems of spectral analysis.