Discretization of certain operators and their spectral and pseudo-spectral study

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dc.contributor.authorDERKAOUI Rafik
dc.date.accessioned2022-10-30T20:14:37Z
dc.date.available2022-10-30T20:14:37Z
dc.date.issued2022-07-03
dc.description.abstractThe project of this thesis treated one of the most important and newest topics in functional analysis. In the present study , we focused on several aspects, such as the theory of spectrum, the demand for this result arise in the solution of linear equations and in many other mathematics and physics problems. The pseudo-spectrum discovered by the numerical scientist Lioyd Nicholas Trefthen in the early of 90s plays an important role in the study of non-normal operators. Also, in order to understand the perturbations of spectral objects, we set a point in pseudo-spectrum. Moreover, we discussed "The Numerical Range of an Operator", particularly the numerical range of matrices, with clarifying examples. The relevant of the latest result that it can be applied to many mathematical disciplines such as the Theory of Linear Operators, Matrix Polynomials, and applications in various fields including C-algebras. In the present work, we studied the discretization of some operators and their spectral and pseudo-spectral studies by providing examples of some operators by resorting to numerical methods. In the first example , we study of the discretization of the operator of Benilov et al, then the spectral and pseudo-spectral study of this discretization, while, in the second example, we discretize the advection-diffusion operator that we have established its spectrum and pseudo-spectrum.
dc.identifier.urihttps://dspace.univ-oran1.dz/handle/123456789/329
dc.language.isoen
dc.subjectBounded Operator
dc.subjectNormal Operator
dc.subjectOscillator group
dc.subjectHeisenberg Group
dc.subjectSpectrum
dc.subjectPseudo-spectrum
dc.subjectNumerical Range
dc.subjectDiscretization of Operator
dc.subjectBenilov Operator
dc.subjectAdvection-diffusion operator
dc.titleDiscretization of certain operators and their spectral and pseudo-spectral study
dc.typeThesis
grade.ExaminateurMessirdi Miloud, Professeur, Université de Tlemcen
grade.ExaminateurKainane Mezzedek Mohamed, MCA, Université de Chlef
grade.ExaminateurDjebbar Bachir, Professeur, USTO
grade.ExaminateurBelaib Lekhmissi, Professeur, Université Oran 1
grade.PrésidentAiboudi Mohamed, Professeur, Université Oran 1
grade.RapporteurSMAIL Abderrahmane, Professeur, Université Oran 1
l'article.1.DateParutionNovembre 2021
l'article.1.RevueCankaya University Journal of Science and Engineering.
l'article.1.RéférenceDERKAOUI Rafik . Numerical Range of Left Invariant Lorentzian Metrics on the Heisenberg Group H₃ of Dimension Three. Cankaya University Journal of Science and Engineering. Novembre 2021
l'article.1.TitreNumerical Range of Left Invariant Lorentzian Metrics on the Heisenberg Group H₃ of Dimension Three.
la.Mentiontrès honorables
la.SpécialitéGéométrie et analyse
la.coteTH5337
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Thèses de Doctorat "Mathématique"