Ognjen Milatovic

Self-Adjoint Extensions of Discrete Magnetic Schrödinger Operators

Using the concept of an intrinsic metric on a locally finite weighted graph, we give sufficient conditions for the magnetic Schrödinger operator to be essentially self-adjoint. The present paper is an extension of some recent results proven in the context of graphs of bounded degree.

Essential Self-adjointness of Magnetic Schrödinger Operators on Locally Finite Graphs

We give sufficient conditions for essential self-adjointness of magnetic Schrödinger operators on locally finite graphs. Two of the main results of the present paper generalize recent results of Torki-Hamza.

Separation property for Schrödinger operators in L p -spaces on non-compact manifolds

Let (M, g) be a manifold of bounded geometry with metric g. We consider a Schrödinger-type differential expression L = Δ M  + q, where Δ M is the scalar Laplacian on M and q is a non-negative locally integrable function on M. In the terminology of W.N. Everitt and M. Giertz, the differential expression L is said to be separated in L p (M) if for all u ∈ L p (M) such that Lu ∈ L p (M), we have qu ∈ L p (M). We give sufficient conditions for L to be separated in L p (M), where 1 < p < ∞.

Self-adjointness of the Gaffney Laplacian on Vector Bundles

We study the Gaffney Laplacian on a vector bundle equipped with a compatible metric and connection over a Riemannian manifold that is possibly geodesically incomplete. Under the hypothesis that the Cauchy boundary is polar, we demonstrate the self-adjointness of this Laplacian. Furthermore, we show that negligible boundary is a necessary and sufficient condition for the self-adjointness of this operator.

ON

Let (M, g) be a manifold of bounded geometry with metric g. We consider a Schrödinger-type differential expression H = ∆M + V , where ∆M is the scalar Laplacian on M and V is a non-negative locally integrable function on M . We give a sufficient condition for H to have an m-accretive realization in the space L(M).

m

We consider a Schrodinger differential expression L0 = ΔM + V0 on a Riemannian manifold (M,g) with metric g, where ΔM is the scalar Laplacian on M and V0 is a real-valued locally square integrable function on M. We consider a perturbation L0 + V, where V is a non-negative locally square-integrable function on M, and give sufficient conditions for L0 + V to be essentially self-adjoint on . This is an extension of a result of T. Kappeler.