Spectral stability of Schrödinger operators with subordinated complex potentials

We prove that the spectrum of Schroedinger operators in three dimensions is purely continuous and coincides with the non-negative semiaxis for all potentials satisfying a form-subordinate smallness condition. By developing the method of multipliers, we also establish the absence of point spectrum fo...

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Detalles Bibliográficos
Autores: Fanelli, L., Krejcirik, D., Vega, L.
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2018
País:España
Institución:Basque Center for Applied Mathematics (BCAM)
Repositorio:BIRD. BCAM's Institutional Repository Data
OAI Identifier:oai:bird.bcamath.org:20.500.11824/824
Acceso en línea:http://hdl.handle.net/20.500.11824/824
Access Level:acceso abierto
Palabra clave:Absence of eigenvalues
Birman-Schwinger principle
Non-self-adjoint Schrödinger operator
Spectral stability
Subordinate complex potential
Technique of multipliers
Descripción
Sumario:We prove that the spectrum of Schroedinger operators in three dimensions is purely continuous and coincides with the non-negative semiaxis for all potentials satisfying a form-subordinate smallness condition. By developing the method of multipliers, we also establish the absence of point spectrum for Schroedinger operators in all dimensions under various alternative hypotheses, still allowing complex-valued potentials with critical singularities.