ON THE ABSOLUTE CONTINUOUS SPECTRUM OF DISCRETE OPERATORS

Sylvain Golenia (1)

1 IMB - Institut de Mathématiques de Bordeaux

This aim of this course is to give an overview to the study of the continuous spectrum of bounded self-adjoint operators and especially those coming from the setting of graphs. For the sake of completeness, a short course in spectral theory is given with proofs. The continuous and Borelian functional calculi are also developed.

Mots clés: commutator theory; Mourre estimate; a.c. spectrum; discrete laplacian; graphs; functional calculi; discrete Dirac operator

Domaines: Théorie spectrale [math.SP]; Analyse fonctionnelle [math.FA]

Sylvain Golenia. ON THE ABSOLUTE CONTINUOUS SPECTRUM OF DISCRETE OPERATORS. Master. Théorie spectrale des graphes et des variétés, Kairouan, Tunisia. 2016, pp.56. ⟨cel-01484506⟩