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Ognjen Milatovic

Publications and source records attributed to Ognjen Milatovic.

21 records · Page 2Linked to original sources
arXiv2012

A Sears-type self-adjointness result for discrete magnetic Schrödinger operators

In the context of a weighted graph with vertex set $V$ and bounded vertex degree, we give a sufficient condition for the essential self-adjointness of the operator $Δ_σ+W$, where $Δ_σ$ is the magnetic Laplacian and $W\colon V\to\mathbb{R}$ is a function satisfying $W(x)\geq -q(x)$ for all $x\in V$, with $q\colon V\to [1,\infty)$. The condition is expressed in terms of completeness of a metric that depends on $q$ and the weights of the graph. The main result is a discrete analogue of the results of I. Oleinik and M. A. Shubin in the setting of non-compact Riemannian manifolds.

math.SP↗
arXiv2002

Essential self-adjointness of Schroedinger type operators on manifolds

We obtain several essential self-adjointness conditions for a Schroedinger type operator D*D+V acting in sections of a vector bundle over a manifold M. Here V is a locally square-integrable bundle map. Our conditions are expressed in terms of completeness of certain metrics on M; these metrics are naturally associated to the operator. We do not assume a priori that M is endowed with a complete Riemannian metric. This allows us to treat e.g. operators acting on bounded domains in the euclidean space. For the case when the principal symbol of the operator is scalar, we establish more precise results. The proofs are based on an extension of the Kato inequality which modifies and improves a result of Hess, Schrader and Uhlenbrock.

math.SP↗