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...
- 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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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 |
dc.type.coar.none.fl_str_mv |
http://purl.org/coar/resource_type/c_db06 |
dc.type.content.none.fl_str_mv |
Text |
dc.type.redcol.none.fl_str_mv |
https://purl.org/redcol/resource_type/TD |
format |
http://purl.org/coar/resource_type/c_db06 |
status_str |
acceptedVersion |
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/ |
dc.rights.accessrights.none.fl_str_mv |
info:eu-repo/semantics/openAccess |
dc.rights.coar.none.fl_str_mv |
http://purl.org/coar/access_right/c_abf2 |
rights_invalid_str_mv |
Attribution 4.0 International http://creativecommons.org/licenses/by/4.0/ 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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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. Next, we consider a Laplacian with quasiperiodic boundary conditions.Doctor en MatemáticasDoctorado84 páginasapplication/pdfengUniversidad de los AndesDoctorado en MatemáticasFacultad de CienciasDepartamento de MatemáticasAttribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Perturbations of normal operators and applicationsTrabajo de grado - Doctoradoinfo:eu-repo/semantics/doctoralThesisinfo:eu-repo/semantics/acceptedVersionhttp://purl.org/coar/resource_type/c_db06Texthttps://purl.org/redcol/resource_type/TDNormal operatorPerturbation TheorySpectral TheorySpectral gapsSpectrumNon-selfadjoint operatorResolvent estimateMatemáticas201628094PublicationORIGINALPerturbations of normal operators and applications.pdfPerturbations of normal operators and 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