7 papers
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…
Spectral minimal partitions of unbounded domains
Matthias Hofmann, James B. Kennedy, Hugo Tavares
We study the problem of constructing -spectral minimal partitions of domains in dimensions, where the energy functional to be minimized is a -norm ()…
Eigenvalues of the discrete p-Laplacian via graph surgery
Gregory Berkolaiko, Matthias Hofmann
We develop a Hellmann--Feynman type perturbation theory for the discrete signed -Laplacian and apply it to a parametrized perturbation by edge cuts. We show that the eigenvalues…
On Courant-type bounds and spectral partitioning via Neumann domains on quantum graphs
Luís Baptista, Matthias Hofmann
We study the structure of eigenfunctions of the Laplacian on quantum graphs, with a particular focus on Morse eigenfunctions via nodal and Neumann domains. Building on Courant-type…
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…
On the existence of Nehari ground states for the Nonlinear Schrödinger Equation on Discrete Graphs
Setenay Akduman, Matthias Hofmann, Sedef Karakılıç
We study standing waves for the nonlinear Schrödinger equation on a discrete graph. We characterize for a self-adjoint realizations of Schrödinger operators conditions related with…
Graph structure of the nodal set and bounds on the number of critical points of eigenfunctions on Riemannian manifolds
Matthias Hofmann, Matthias Täufer
In this article, we illustrate and draw connections between the geometry of zero sets of eigenfunctions, graph theory and the vanishing order of eigenfunctions. We identify the nod…