37 citations · 124 across the 19 of their papers we have counts for
22 papers
Eigenvalue asymptotics and unique continuation of eigenfunctions on planar graphs
Michel Bonnefont, Sylvain Golenia, Matthias Keller
We study planar graphs with large negative curvature outside of a finite set and the spectral theory of Schr{ö}dinger operators on these graphs. We obtain estimates on the first an…
Bands of pure a.c. spectrum for lattice Schr{ö}dinger operators with a more general long range condition. Part I
Sylvain Golenia, Marc Adrien Mandich
Commutator methods are applied to get limiting absorption principles for the discrete standard and Molchanov-Vainberg Schrödinger operators and $H_{\mathrm{…
The Essential Spectrum of the Discrete Laplacian on Klaus-sparse Graphs
Sylvain Golenia, Françoise Truc
In 1983, Klaus studied a class of potentials with bumps and computed the essential spectrum of the associated Schr{ö}dinger operator with the help of some localisations at infinity…
Limiting absorption principle for discrete Schr{ö}dinger operators with a Wigner-von Neumann potential and a slowly decaying potential
Sylvain Golenia, Marc-Adrien Mandich
We consider discrete Schr{ö}dinger operators on for which the perturbation consists of the sum of a long-range type potential and a Wigner-von Neumann type potenti…
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…
Magnetic sparseness and Schrödinger operators on graphs
Michel Bonnefont, Sylvain Golénia, Matthias Keller +2
We study magnetic Schrödinger operators on graphs. We extend the notion of sparseness of graphs by including a magnetic quantity called the frustration index. This notion of magnet…