Non-accretive Schrödinger operators and exponential decay of their eigenfunctions

David Krejcirik (1) , Nicolas Raymond (2) , Julien Royer (3) , Petr Siegl (4)

1 Nuclear Physics Institute ASCR
2 IRMAR - Institut de Recherche Mathématique de Rennes
3 IMT - Institut de Mathématiques de Toulouse UMR5219
4 IMSV - Institute of Mathematical Statistics and Actuarial Science [Bern]

We consider non-self-adjoint electromagnetic Schrödinger operators on arbitrary open sets with complex scalar potentials whose real part is not necessarily bounded from below. Under a suitable sufficient condition on the electromagnetic potential, we introduce a Dirichlet realisation as a closed densely defined operator with non-empty resolvent set and show that the eigenfunctions corresponding to discrete eigenvalues satisfy an Agmon-type exponential decay.

Domaines: Théorie spectrale [math.SP]

David Krejcirik, Nicolas Raymond, Julien Royer, Petr Siegl. Non-accretive Schrödinger operators and exponential decay of their eigenfunctions. Israel Journal of Mathematics, 2017, 221 (2), pp.779-802. ⟨10.1007/s11856-017-1574-z⟩. ⟨hal-01310683⟩