Laplaciens de graphes infinis I Graphes métriquement complets

Details Laplaciens de graphes infinis I Graphes métriquement complets Laplaciens de graphes infinis I Graphes métriquement complets

2010-06-25

arxiv.org/abs/1006.4993v1

Confluentes Mathematici (CM) 2, 3 (2010) 333-350

Mathematics

Spectral Theory

Scientific paper

10.1142/S179374421000020X

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 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

Laplaciens de graphes infinis I Graphes métriquement complets 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 Laplaciens de graphes infinis I Graphes métriquement complets, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Laplaciens de graphes infinis I Graphes métriquement complets will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-310221