On the completeness of root function system of the Dirac operator with two-point boundary conditions

TL;DR

This paper investigates the completeness of root functions for the Dirac operator with complex potentials and non-regular boundary conditions, providing explicit fundamental solutions.

Contribution

It establishes the completeness of root functions and derives explicit fundamental solutions for the Dirac operator under complex potentials and non-regular boundary conditions.

Findings

Proves the completeness of root functions.

Derives explicit fundamental solution system.

Abstract

The paper is concerned with the completeness property of root functions of the Dirac operator with summable complexvalued potential and non-regular boundary conditions. We also obtain explicit form for the fundamental solution system of the considered operator.