Catalogue des ouvrages Université de Laghouat
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| Titre : | Studies of some operators between model spaces | | Type de document : | document multimédia | | Auteurs : | Said Benslimane, Auteur ; Ameur Yagoub, Directeur de thèse | | Editeur : | Laghouat : Université Amar Telidji - Département de mathématiques | | Année de publication : | 2025 | | Importance : | 75 p. | | Accompagnement : | 1 disque optique numérique (CD-ROM) | | Note générale : | Option : Functional analysis | | Langues : | Anglais | | Résumé : | This thesis falls within the field of operator theory in model spaces.It is divided into two main parts,each addressing fundamental aspects of asymmetric truncated Toeplitz (Hankel) operators and rectangular Toeplitz (Hankel) matrices.
In the first part, we focus on the study of asymmetric truncated Toeplitz (Hankel) operators in amodel space.We establish the necessary and sufficient conditions under which the product of two such operators remains an asymmetric truncated Toeplitz (Hankel)operator.This analysis provides deeper in sight into the structural properties and algebraic behavior of the seoperators.
In the second part,we shift our attentio nto rectangular Toeplitz (Hankel) matrices.
We derive the necessary and sufficient conditions for the product of two such matrices to retain the Toeplitz(Hankel)structure. Additionally,we investigate the conditions under whicha rectangular Toeplitz (Hankel) matrix is isometric,further enriching the understanding of the sestructured matrices in the broader context of operator theory.
Through these studies,this thesis contributes to the on going exploration of structured operators and matrices,shedding light on their fundamental properties and interactions. | | note de thèses : | Thèse de doctorat en mathématiques |
Studies of some operators between model spaces [document multimédia] / Said Benslimane, Auteur ; Ameur Yagoub, Directeur de thèse . - Laghouat : Université Amar Telidji - Département de mathématiques, 2025 . - 75 p. + 1 disque optique numérique (CD-ROM). Option : Functional analysis Langues : Anglais | Résumé : | This thesis falls within the field of operator theory in model spaces.It is divided into two main parts,each addressing fundamental aspects of asymmetric truncated Toeplitz (Hankel) operators and rectangular Toeplitz (Hankel) matrices.
In the first part, we focus on the study of asymmetric truncated Toeplitz (Hankel) operators in amodel space.We establish the necessary and sufficient conditions under which the product of two such operators remains an asymmetric truncated Toeplitz (Hankel)operator.This analysis provides deeper in sight into the structural properties and algebraic behavior of the seoperators.
In the second part,we shift our attentio nto rectangular Toeplitz (Hankel) matrices.
We derive the necessary and sufficient conditions for the product of two such matrices to retain the Toeplitz(Hankel)structure. Additionally,we investigate the conditions under whicha rectangular Toeplitz (Hankel) matrix is isometric,further enriching the understanding of the sestructured matrices in the broader context of operator theory.
Through these studies,this thesis contributes to the on going exploration of structured operators and matrices,shedding light on their fundamental properties and interactions. | | note de thèses : | Thèse de doctorat en mathématiques |
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