Abstract:

The study of non-self-adjoint differential operators is a historical issue. Before and until now, most studies of operator theory have been about self-adjoint operators. But non-self-adjoint operators have recently found many applications in other sciences. These operators have received much attention in thermodynamics and quantum mechanics. Because there is no general spectral theory for these operators, it is more difficult to study these operators than the self-adjoint type. The spectrum of these operators is usually unstable and their resolvent is unpredictable. In this paper, a second-order non-self-attached differential operator is considered and its spectral properties and solvent estimation are studied. This operator is much more common than second-tier operators such as Storm-Liouville and Schrodinger.

Keywords: