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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Bibliographic Details
Author: Martínez, C
Format: article
Status:Published version
Publication Date:2006
Country:México
Institution:Universidad Nacional Autónoma de México
Repository:Sistema de Información de la Facultad de Ciencias, UNAM
OAI Identifier:oai:repositorio.fciencias.unam.mx:11154/1251
Online Access:http://hdl.handle.net/11154/1251
Access Level:Open access
Keyword:Mathematics
Anderson model
non-self-adjoint operator
spectrum
numerical range
ergodic operator
Description
Summary: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.