25 citations · 158 across the 37 of their papers we have counts for
11 papers · 1 filter
Ambarzumian-type theorems for Hermitian matrices with applications
Matthias Hofmann, Joachim Kerner
A foundational result in inverse spectral theory due to Ambarzumian (1929) states that the Neumann Laplacian on an interval is not isospectral to the Neumann Laplacian with an addi…
On the asymptotic behavior of the spectral gap for discrete Schrödinger operators
Matthias Hofmann, Joachim Kerner, Maximilian Pechmann
In this note we elaborate on the asymptotic behavior of the spectral gap of a class of discrete Schrödinger operators defined on a path graph in the limit of infinite volume. We co…
Some spectral comparison results on infinite quantum graphs
Patrizio Bifulco, Joachim Kerner
In this paper we establish spectral comparison results for Schrödinger operators on a certain class of infinite quantum graphs, using recent results obtained in the finite setting.…
A note on Ambarzumian's theorem for quantum graphs
Patrizio Bifulco, Joachim Kerner
Based on the main result presented in a recent paper, we derive Ambarzumian-type theorems for Schrödinger operators defined on quantum graphs. We recover existing results such as t…
Robustness of flat bands on the perturbed Kagome and the perturbed Super-Kagome lattice
Joachim Kerner, Matthias Täufer, Jens Wintermayr
We study spectral properties of perturbed discrete Laplacians on two-dimensional Archimedean tilings. The perturbation manifests itself in the introduction of non-trivial edge weig…
On the spectral gap of higher-dimensional Schrödinger operators on large domains
Joachim Kerner, Matthias Täufer
We study the asymptotic behaviour of the spectral gap of Schrödinger operators in two and higher dimensions and in a limit where the volume of the domain tends to infinity. Dependi…
On the spectral gap of the path graph in the limit of large volume
Joachim Kerner, Pavlo Yatsyna
In this paper we study the spectral gap of the path graph and illustrate an interesting effect which has been described recently in the continuous setting. More explicitly, in the…
A lower bound on the spectral gap of one-dimensional Schrödinger operators
Joachim Kerner
In this note we provide an explicit lower bound on the spectral gap of one-dimensional Schrödinger operators with non-negative bounded potentials and subject to Neumann boundary co…
A lower bound on the spectral gap of Schrödinger operators with weak potentials of compact support
Joachim Kerner
In this paper we continue the study of the spectral gap of Schrödinger operators on large intervals and subject to Neumann boundary conditions. The main goal is to derive a lower b…
On the spectral gap of one-dimensional Schrödinger operators on large intervals
Joachim Kerner, Matthias Täufer
We study the effect of non-negative potentials on the spectral gap of one-dimensional Schrödinger operators in the limit of large intervals. In particular, we derive upper and lowe…
Numerical range with respect to a family of projections
W. Dada, N. Erkurşun, J. Kerner
In this note we introduce the concept of the numerical range of a bounded linear operator with respect to a family of projections. We give a precise definition and elaborate on its…