Spectral Analysis of 1D Dirac System with Summable Potential and Sturm–Liouville Operator with Distribution Coefficients

In the paper we study the spectral properties of Sturm-Liouville and Dirac operators.Both operators are considered on a finite segment. The potential of the Sturm–Liouville operatoris assumed to be a distribution of first order singularity, and the potential of the Dirac operator isassumed to be a summable function. The boundary conditions are assumed to be Birkhoff regular.The main results are about the resolvent of both operators, the properties of the spectrum, theasymptotics of eigen- and associated functions, the completeness and basicity (conditional andunconditional) of these systems, and the equiconvergence of spectral decompositions.