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Laplaciens de graphes infinis I Graphes m'etriquement complets | Nabila Torki-Hamza
; | Date: |
25 Jun 2010 | Abstract: | 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. | Source: | arXiv, 1006.4993 | Services: | Forum | Review | PDF | Favorites |
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