Perturbations of normal operators and applications

We present some new results for normal operators. We study the effect of relatively bounded perturbations on the spectrum of normal operators and present stability results for spectral gaps considering the spectrum of the unperturbated operator is close to the real axis or it is contained in a secto...

Full description

Autores:
Moreno Paris, Javier David
Tipo de recurso:
Doctoral thesis
Fecha de publicación:
2023
Institución:
Universidad de los Andes
Repositorio:
Séneca: repositorio Uniandes
Idioma:
eng
OAI Identifier:
oai:repositorio.uniandes.edu.co:1992/73870
Acceso en línea:
https://hdl.handle.net/1992/73870
Palabra clave:
Normal operator
Perturbation Theory
Spectral Theory
Spectral gaps
Spectrum
Non-selfadjoint operator
Resolvent estimate
Matemáticas
Rights
openAccess
License
Attribution 4.0 International
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oai_identifier_str oai:repositorio.uniandes.edu.co:1992/73870
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dc.title.eng.fl_str_mv Perturbations of normal operators and applications
title Perturbations of normal operators and applications
spellingShingle Perturbations of normal operators and applications
Normal operator
Perturbation Theory
Spectral Theory
Spectral gaps
Spectrum
Non-selfadjoint operator
Resolvent estimate
Matemáticas
title_short Perturbations of normal operators and applications
title_full Perturbations of normal operators and applications
title_fullStr Perturbations of normal operators and applications
title_full_unstemmed Perturbations of normal operators and applications
title_sort Perturbations of normal operators and applications
dc.creator.fl_str_mv Moreno Paris, Javier David
dc.contributor.advisor.none.fl_str_mv Winklmeier, Monika Anna
dc.contributor.author.none.fl_str_mv Moreno Paris, Javier David
dc.contributor.jury.none.fl_str_mv Boegli, Sabine
Cuenin, Jean-Claude
Cortissoz Iriarte, Jean Carlos
dc.subject.keyword.none.fl_str_mv Normal operator
Perturbation Theory
Spectral Theory
Spectral gaps
Spectrum
Non-selfadjoint operator
Resolvent estimate
topic Normal operator
Perturbation Theory
Spectral Theory
Spectral gaps
Spectrum
Non-selfadjoint operator
Resolvent estimate
Matemáticas
dc.subject.themes.spa.fl_str_mv Matemáticas
description We present some new results for normal operators. We study the effect of relatively bounded perturbations on the spectrum of normal operators and present stability results for spectral gaps considering the spectrum of the unperturbated operator is close to the real axis or it is contained in a sector symmetric to the real axis. we do not assume that the perturbation is symmetric or normal. Moreover, we established stability results for spectral gaps, essential spectrum gaps, algebraic multiplicities and estimates for the resolvent. If the perturbation is even p-subordinate to the normal operator, then we obtain stronger results for the localisation of the spectrum. Finally, we apply some of our results to Schrödinger operators. First, we consider a Laplacian defined on quantum star graph with non-selfadjoint boundary conditions. Next, we consider a Laplacian with quasiperiodic boundary conditions.
publishDate 2023
dc.date.issued.none.fl_str_mv 2023-11-30
dc.date.accessioned.none.fl_str_mv 2024-02-02T22:09:35Z
dc.date.available.none.fl_str_mv 2024-02-02T22:09:35Z
dc.type.none.fl_str_mv Trabajo de grado - Doctorado
dc.type.driver.none.fl_str_mv info:eu-repo/semantics/doctoralThesis
dc.type.version.none.fl_str_mv info:eu-repo/semantics/acceptedVersion
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dc.identifier.uri.none.fl_str_mv https://hdl.handle.net/1992/73870
dc.identifier.doi.none.fl_str_mv 10.57784/1992/73870
dc.identifier.instname.none.fl_str_mv instname:Universidad de los Andes
dc.identifier.reponame.none.fl_str_mv reponame:Repositorio Institucional Séneca
dc.identifier.repourl.none.fl_str_mv repourl:https://repositorio.uniandes.edu.co/
url https://hdl.handle.net/1992/73870
identifier_str_mv 10.57784/1992/73870
instname:Universidad de los Andes
reponame:Repositorio Institucional Séneca
repourl:https://repositorio.uniandes.edu.co/
dc.language.iso.none.fl_str_mv eng
language eng
dc.rights.en.fl_str_mv Attribution 4.0 International
dc.rights.uri.none.fl_str_mv http://creativecommons.org/licenses/by/4.0/
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http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.extent.none.fl_str_mv 84 páginas
dc.format.mimetype.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Universidad de los Andes
dc.publisher.program.none.fl_str_mv Doctorado en Matemáticas
dc.publisher.faculty.none.fl_str_mv Facultad de Ciencias
dc.publisher.department.none.fl_str_mv Departamento de Matemáticas
publisher.none.fl_str_mv Universidad de los Andes
institution Universidad de los Andes
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spelling Winklmeier, Monika AnnaMoreno Paris, Javier DavidBoegli, SabineCuenin, Jean-ClaudeCortissoz Iriarte, Jean Carlos2024-02-02T22:09:35Z2024-02-02T22:09:35Z2023-11-30https://hdl.handle.net/1992/7387010.57784/1992/73870instname:Universidad de los Andesreponame:Repositorio Institucional Sénecarepourl:https://repositorio.uniandes.edu.co/We present some new results for normal operators. We study the effect of relatively bounded perturbations on the spectrum of normal operators and present stability results for spectral gaps considering the spectrum of the unperturbated operator is close to the real axis or it is contained in a sector symmetric to the real axis. we do not assume that the perturbation is symmetric or normal. Moreover, we established stability results for spectral gaps, essential spectrum gaps, algebraic multiplicities and estimates for the resolvent. If the perturbation is even p-subordinate to the normal operator, then we obtain stronger results for the localisation of the spectrum. Finally, we apply some of our results to Schrödinger operators. First, we consider a Laplacian defined on quantum star graph with non-selfadjoint boundary conditions. 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