4 papers
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\|…
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…
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…