Related papers: Probabilistic characterizations of essential self-…

We give two characterizations for the essential self-adjointness of the weighted Laplacian on birth-death chains. The first involves the edge weights and vertex measure and is classically known; however, we give another proof using…

We discuss connections between the essential self-adjointness of a symmetric operator and the constancy of functions which are in the kernel of the adjoint of the operator. We then illustrate this relationship in the case of Laplacians on…

We study Laplacians on general countable weighted simplicial complexes from a conceptual point of view. These operators will first be introduced formally before showing that those formal operators coincide with self-adjoint realizations of…

We prove a general essential self-adjointness criterion for sub-Laplacians on complete sub-Riemannian manifolds, defined with respect to singular measures. As a consequence, we show that the intrinsic sub-Laplacian (i.e. defined w.r.t.…

In this paper, we define the structure of $n$-simplicial complex, we consider generalizations of the Laplacians to simplicial complexes of higher dimension and we develop the notion of $\chi$-completeness for simplicial complexes.…

The self-adjointness of the reduced Hamiltonian operators arising from the Laplace-Beltrami operator of a complete Riemannian manifold through quantum Hamiltonian reduction based on a compact isometry group is studied. A simple sufficient…

Let $\Omega_-$ and $\Omega_+$ be two bounded smooth domains in $\mathbb{R}^n$, $n\ge 2$, separated by a hypersurface $\Sigma$. For $\mu>0$, consider the function $h_\mu=1_{\Omega_-}-\mu 1_{\Omega_+}$. We discuss self-adjoint realizations of…

For a class of singular potentials, including the Coulomb potential (in three and less dimensions) and $V(x) = g/x^2$ with the coefficient $g$ in a certain range ($x$ being a space coordinate in one or more dimensions), the corresponding…

This paper is devoted to the study of essential self-adjointness of a relativistic Schr\"{o}dinger operator with a singular homogeneous potential. From an explicit condition on the coefficient of the singular term, we provide a sufficient…

We establish explicit operator norm bounds and essential self-adjointness criteria for discrete Hodge Laplacians on weighted graphs and simplicial complexes. For unweighted $d$-regular graphs we prove the universal estimate…

We consider first-order differential operators with locally bounded measurable coefficients on vector bundles with measurable coefficient metrics. Under a mild set of assumptions, we demonstrate the equivalence between the essential…

Form methods are most efficient to prove generation theorems for semigroups but also for proving selfadjointness. So far those theorems are based on a coercivity notion which allows the use of the Lax-Milgram Lemma. Here we consider weaker…

We study symmetric diffusion operators on metric measure spaces. Our main question is whether or not the restriction of the operator to a suitable core continues to be essentially self-adjoint or $L^p$-unique if a small closed set is…

We give a sufficient condition for the essential self-adjointness of a perturbation of the square of the magnetic Laplacian on an infinite weighted graph. The main result is applicable to graphs whose degree function is not necessarily…

We deal with the random combinatorial structures called assemblies. By weakening the logarithmic condition which assures regularity of the number of components of a given order, we extend the notion of logarithmic assemblies. Using the…

We prove essential self-adjointness for semi-bounded below magnetic Schr\"odinger operators on complete Riemannian manifolds with a given positive smooth measure which is fixed independently of the metric. Some singularities of the scalar…

In the paper we represent two examples which are based on the properties of discrete measures. In the first part of the paper we prove that for each probability measure $\mu$, $\operatorname{supp}{\mu}=[-1,1]$, which logarithmic potential…

We study the relationship between the adjacency matrix and the discrete Laplacian acting on 1-forms. We also prove that if the adjacency matrix is bounded from below it is not necessarily essentially self-adjoint. We discuss the question of…

It is shown the stability of the essential self-adjointness, and an inclusion of the essential spectra of Laplacians under the change of Riemannian metric on a subset K of M. The set K may have infinite volume measured with the new metric…

We characterize exactly the compactness properties of the product of \kappa\ copies of the space \omega\ with the discrete topology. The characterization involves uniform ultrafilters, infinitary languages, and the existence of nonstandard…