Related papers: Essential self-adjointness of the Laplacian on wei…
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 introduce the weighted graph Laplacian and the notion of Schr\"odinger operator on a locally finite weighted graph. Concerning essential self-adjointness, we extend Wojciechowski's and Dodziuk's results for graphs with vertex constant…
We study the essential self-adjointness of semi-bounded Schr\"{o}dinger operators on birth-death chains. First, we offer a general characterization which originates from studying a second order linear recurrence with variational…
We introduce the weighted graph Laplacian and the notion of Schr\"odinger operator on a locally finite weighted graph . Concerning essential self-adjointness, we extend Wojciechowski's and Dodziuk's results for graphs with vertex constant…
We consider weighted graphs, we equip them with a metric structure given by a weighted distance, and we discuss essential self-adjointness for weighted graph Laplacians and Schr\"odinger operators in the metrically non complete case.
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 consider the Laplacian and its fractional powers of order less than one on the complement $\mathbb{R}^d\setminus\Sigma$ of a given compact set $\Sigma\subset \mathbb{R}^d$ of zero Lebesgue measure. Depending on the size of $\Sigma$, the…
We define the magnetic Schr\"odinger on an infinite graph by the data of a magnetic field, some weights on vertices and some weights on edges . We discuss essential self-adjointness of this operator for graphs of bounded degree. The main…
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 study the uniqueness of self-adjoint and Markovian extensions of the Laplacian on weighted graphs. We first show that, for locally finite graphs and a certain family of metrics, completeness of the graph implies uniqueness of these…
We consider a non self-adjoint Laplacian on a directed graph with non symmetric edge weights. We give necessary conditions for this Laplacian to be sectorial. We introduce a special self-adjoint operator and compare its essential spectrum…
We work in the setting of infinite, not necessarily locally finite, weighted graphs. We give a sufficient condition for the essential self-adjointness of (discrete) Schr\"odinger operators $\mathcal{L}_{V}$ that are not necessarily lower…
This paper deals with spectral graph theory issues related to questions of monotonicity and comparison of eigenvalues. We consider finite directed graphs with non symmetric edge weights and we introduce a special self-adjoint operator as…
We consider a non self-adjoint Laplacian on a directed graph with non symmetric edge weights. We analyse spectral properties of this Laplacian under a Kirchhoff assumption. Moreover we establish isoperimet-ric inequalities in terms of the…
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.…
This work explores the definiteness of the weighted graph Laplacian matrix with negative edge weights. The definiteness of the weighted Laplacian is studied in terms of certain matrices that are related via congruent and similarity…
We study the operator theory associated with such infinite graphs $G$ as occur in electrical networks, in fractals, in statistical mechanics, and even in internet search engines. Our emphasis is on the determination of spectral data for a…
We give sufficient conditions for essential self-adjointness of magnetic Schr\"odinger operators on locally finite graphs. Two of the main theorems of the present paper generalize recent results of Torki-Hamza.
We study Laplacians associated to a graph and single out a class of such operators with special regularity properties. In the case of locally finite graphs, this class consists of all selfadjoint, non-negative restrictions of the standard…
On finite metric graphs we consider Laplace operators, subject to various classes of non-self-adjoint boundary conditions imposed at graph vertices. We investigate spectral properties, existence of a Riesz basis of projectors and similarity…