The inverse spectral problem for the Sturm-Liouville operators with discontinuous coefficients.
We discuss the spectral properties of the operator on the line. We first briefly describe how this operator appears in various problems in the analysis of operators on nilpotent Lie groups, in the spectral properties of a Schrödinger operator with magnetic field and in superconductivity. We then give a new proof that the minimum over α of the groundstate energy is attained at a unique point and also prove that the minimum is non-degenerate. Our study can also be seen as a refinement for a specific...
We generalize a well-known separation condition of Everitt and Giertz to a class of weighted symmetric partial differential operators defined on domains in . Also, for symmetric second-order ordinary differential operators we show that where is a singular point guarantees separation of on its minimal domain and extend this criterion to the partial differential setting. As a particular example it is shown that is separated on its minimal domain if is superharmonic. For the criterion...