Petru Cojuhari

Finiteness of Eigenvalues of the Perturbed Dirac Operator

Finiteness criteria are established for the point spectrum of the perturbed Dirac operator. The results are obtained by applying the direct methods of the perturbation theory of linear operators. The particular case of the Hamiltonian of a Dirac particle in an electromagnetic field is also considered.

The Problem of the Finiteness of the Point Spectrum for Self-adjoint Operators. Perturbations of Wiener-Hopf Operators and Applications to Jacobi Matrices

The purpose of this paper is to study the point spectrum for the case of self-adjoint operators. Based on the direct methods of the perturbation theory, sufficient conditions for the finiteness of the point spectrum of some self-adjoint operators are established. The problem is treated for the general case of abstract operators and then, as applications, some concrete classes of operators are investigated. In particular, operators associated to Jacobi type matrices are also considered.