Spectral Analysis of 1D Dirac System with Summable Potentialand Sturm–Liouville Operatorwith 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 operator is assumed to be a distribution of first order singularity, and the potential of the Dirac operator is assumed 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, the asymptotics of eigen- and associated functions, the completeness and basicity (conditional and unconditional) of these systems, and the equiconvergence of spectral decompositions.