Dirac system with a singularity in an interior point

Abstract

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 Stokes multipliers is established. These fundamental systems of solutions will be used for studying direct and inverse problems of spectral analysis.

Keywords:

• Differential systems
• singularity
• spectral analysis

AMS Subject Classifications:

• 34L40
• 34A36
• 47E05

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the Russian Ministry of Education and Science [grant number 1.1436.2014K], Russian Foundation for Basic Research [grant number 13-01-00134], and Mathematics Research Promotion Center of Taiwan [grant number 103-82].