Essential self-adjointness for combinatorial Schrödinger operators I- Metrically complete graphs

Details Essential self-adjointness for combinatorial Schrödinger operators I- Metrically complete graphs Essential self-adjointness for combinatorial Schrödinger operators I- Metrically complete graphs

2012-01-23

arxiv.org/abs/1201.4644v1

Mathematics

Spectral Theory

It is an English updated version of: " Laplaciens de graphes infinis I Graphes m\'etriquement complets", Confluentes Mathemati

Scientific paper

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 weight. The main result in this work states that on any metrically complete weighted graph with bounded degree, the weighted graph Laplacian is essentially self-adjoint and the same holds for the Schr\"odinger operator provided the associated quadratic form is bounded from below. We construct for the proof a strictly positive and harmonic function which allows us to write any Schr\"odinger operator as a weighted graph Laplacian modulo a unitary transform.

Affiliated with

Also associated with

No associations

Rating

Essential self-adjointness for combinatorial Schrödinger operators I- Metrically complete graphs does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Essential self-adjointness for combinatorial Schrödinger operators I- Metrically complete graphs, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Essential self-adjointness for combinatorial Schrödinger operators I- Metrically complete graphs will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-496979