13 papers
Study of Rota-Baxter Operators in Matrix -Algebras Motivated by Toeplitz Structures, and Applications to Sliding Mode Control
Marwa Ennaceur
This paper studies Rota-Baxter operators on the matrix -algebra , motivated by the discrete Toeplitz algebra (whose role is purely heuristic; see Remark~\ref{…
Local Lie Theory in Quasi-Banach Lie Algebras: Convergence of the BCH Series and Geometric Implications
Nassim Athmouni, Mohsen Ben Abdallah, Mondher Damak +3
We develop a local Lie theory for Lie algebras equipped with a quasi-norm, i.e., complete topological vector spaces satisfying a relaxed triangle inequality $\|x+y\|\le \Ctri(\|x\|…
Spectral Theory of Almost Periodic Banach--Malcev Algebras and Applications to Moufang Dynamics
Marwa Ennaceur
We introduce almost periodic Banach--Malcev algebras as a non-associative extension of Bohr's classical theory. Our framework is based on the relative compactness of adjoint orbits…
Homogeneous Rota--Baxter Operators of Weight~0 on
Mohsen Ben Abdallah, Marwa Ennaceur
We give a complete and rigorous classification of homogeneous weight Rota--Baxter operators on the Block-type Witt algebra , assuming the operator has integral degree $(k…
Classification of Homogeneous Odd Rota--Baxter Operators on a Modified Witt-Type Lie Superalgebra
Mohsen Ben Abdallah, Marwa Ennaceur
We classify all homogeneous odd (i.e., parity-reversing) Rota--Baxter operators of weight zero on the modified Witt-type Lie superalgebra .…
Spectral Theory and Almost Periodic Structures in Hom--Lie Banach Algebras
Marwa Ennaceur
We develop a systematic functional-analytic framework for Hom--Lie Banach algebras, introducing bounded -twisted derivations and almost periodic elements. Under natural continui…
Sharp Ascent--Descent Spectral Stability under Strong Resolvent Convergence
Marwa Ennaceur
We establish sharp stability results for of non--selfadjoint the ascent and descent spectra under strong resolvent convergence (SRS), a natural framework for finite element approxi…
Geometric Criteria for Essential Self-Adjointness of Discrete Hodge Laplacians on Weighted Simplicial Complexes
Marwa Ennaceur, Amel Jadlaoui
We develop a geometric framework for the essential self-adjointness (ESA) of discrete Hodge Laplacians on weighted simplicial complexes of arbitrary dimension. Three notions of …
Hodge Laplacians on Weighted Simplicial Complexes: Forms, Closures, and Bounded Realizations
Marwa Ennaceur, Amel Jadlaoui
We establish operator-norm bounds for discrete Hodge Laplacians on weighted flag complexes of a fixed dimension , whose -simplices are the -cliques of a weighted graph…
Spectral analysis of The magnetic Laplacian acting on discrete funnels
Nassim Athmouni, Marwa Ennaceur, Sylvain Golénia
We study perturbations of the discrete magnetic Laplacian associated to discrete analogs of funnels. We perturb the metric in a long-range way. We establish a propagation estimate…
Limiting absorption principle for long-range perturbation in a graphene setting
Nassim Athmouni, Marwa Ennaceur, Sylvain Golenia +1
In this paper, we examine the discrete Laplacian acting on a hexagonal lattice by introducing long-range modifications in both the metric and the potential. Our objective is to est…
Limiting absorption principle for long-range perturbation in the discrete triangular lattice setting
Nassim Athmouni, Marwa Ennaceur, Sylvain Golenia +1
We examine the discrete Laplacian acting on a triangular lattice, introducing long-range perturbations to both the metric and the potential. Our goal is to establish a Limiting Abs…
Spectral analysis of the Laplacian acting on discrete cusps and funnels
Nassim Athmouni, Marwa Ennaceur, Sylvain Golenia
We study perturbations of the discrete Laplacian associated to discrete analogs of cusps and funnels. We perturb the metric and the potential in a long-range way. We establish a pr…