On the discreteness of the spectrum of matrix Schrödinger and Dirac operators with point interactions (Q2063689)

The paper deals with certain symmetric Jacobi operators with the same deficiency indices. The spectrum of the self-adjoint extensions of these operators is discrete. Based on the correspondence of these Jacobi operators with the matrix Schrödinger operators on \(L^2(\mathbb{R}_+, \mathbb{C}^m)\) with the \(\delta\)-point interactions and the Dirac matrix operators with the \(\delta\)-point interactions on \(L^2((0,b),\mathbb{C}^{2m})\), \(b\leq \infty\) proven in other papers, the authors prove that the Schrödinger and Dirac operators are under certain conditions self-adjoint and their spectra are discrete. If these operators are not self-adjoint, their self-adjoint extensions have discrete spectra.