Spectral estimates for the one-dimensional non-self-adjoint Anderson model

We obtain bounds on the spectrum of the non-self-adjoint Anderson operator in one dimension by using higher order numerical ranges and are able to determine the spectrum completely in many cases. We also develop further some previously existing methods that allow us to prove that certain curves and...

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Detalles Bibliográficos
Autor: Martínez, C
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2006
País:México
Institución:Universidad Nacional Autónoma de México
Repositorio:Sistema de Información de la Facultad de Ciencias, UNAM
OAI Identifier:oai:repositorio.fciencias.unam.mx:11154/1251
Acceso en línea:http://hdl.handle.net/11154/1251
Access Level:acceso abierto
Palabra clave:Mathematics
Anderson model
non-self-adjoint operator
spectrum
numerical range
ergodic operator
Descripción
Sumario:We obtain bounds on the spectrum of the non-self-adjoint Anderson operator in one dimension by using higher order numerical ranges and are able to determine the spectrum completely in many cases. We also develop further some previously existing methods that allow us to prove that certain curves and regions are contained in the spectrum and provide numerical examples that suggest that these curves contained in the infinite volume spectrum have a strong bearing over the finite volume cases.