Self-adjoint extensions of discrete magnetic Schrödinger operators

Francoise Truc (1) , Ognjen Milatovic (2)

1 IF - Institut Fourier
2 UNF - University of North Florida [Jacksonville]

Using the concept of intrinsic metric on a locally finite weighted graph, we give sufficient conditions for the magnetic Schrödinger operator to be essentially self-adjoint. The present paper is an extension of some recent results proven in the context of graphs of bounded degree.

Keywords: Discrete magnetic Schrödinger operator; Essential self-adjointness; Infinite graphs; Intrinsic metric

Domains: Mathematical Physics [math-ph]; Spectral Theory [math.SP]; Functional Analysis [math.FA]

Francoise Truc, Ognjen Milatovic. Self-adjoint extensions of discrete magnetic Schrödinger operators. Annales Henri Poincaré, 2014, 15 (5), pp.917-936. ⟨10.1007/s00023-013-0261-9⟩. ⟨hal-00747698v2⟩