Essential self-adjointness for combinatorial Schrödinger operators II- Metrically non complete graphs

Yves Colin de Verdière (1) , Nabila Torki-Hamza (2, 3) , Francoise Truc (1)

1 IF - Institut Fourier
2 ISIG-K - Institut Supérieur d'Informatique et de Gestion de Kairouan
3 05/UR/15-02 - Mathématiques et Applications

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 Schrödinger operators in the metrically non complete case.

Mots clés: essential selfadjointness; Metrically non complete graph; weighted graph Laplacian; Schrödinger operator; essential selfadjointness.

Domaines: Théorie spectrale [math.SP]

Yves Colin de Verdière, Nabila Torki-Hamza, Francoise Truc. Essential self-adjointness for combinatorial Schrödinger operators II- Metrically non complete graphs. Mathematical Physics Analysis and Geometry, 2011, 14 (1), pp.21-38. ⟨10.1007/s11040-010-9086-7⟩. ⟨hal-00496165v3⟩