The Spectrum of Hill's Equation.
The spectrum of the damped wave operator for a bounded domain in .
The Sturm-Liouville Friedrichs extension
The characterization of the domain of the Friedrichs extension as a restriction of the maximal domain is well known. It depends on principal solutions. Here we establish a characterization as an extension of the minimal domain. Our proof is different and closer in spirit to the Friedrichs construction. It starts with the assumption that the minimal operator is bounded below and does not directly use oscillation theory.
The width of resonances for slowly varying perturbations of one-dimensional periodic Schrödinger operators
Théorème de Paley-Wiener associé à un opérateur différentiel singulier sur
Towards finite-gap integration of the Inozemtsev model.
Transformation operators and asymptotic formulas for the eigenvalues of a polynomial pencil of Sturm--Liouville operators.
Transitions d’Anderson pour des opérateurs de Schrödinger quasi-périodiques en dimension 1
Two new finite difference methods for computing eigenvalues of a fourth order linear boundary value problem.
Two separation criteria for second order ordinary or partial differential operators
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...