27 citations · 166 across the 39 of their papers we have counts for
18 papers · 1 filter
Agmon estimates for Schrödinger operators on graphs
Matthias Keller, Felix Pogorzelski
We prove decay estimates for generalized eigenfunctions of discrete Schrödinger operators on weighted infinite graphs in the spirit of Agmon.
Sobolev-Type Inequalities and Eigenvalue Growth on Graphs with Finite Measure
Bobo Hua, Matthias Keller, Michael Schwarz +1
In this note we study the eigenvalue growth of infinite graphs with discrete spectrum. We assume that the corresponding Dirichlet forms satisfy certain Sobolev-type inequalities an…
Courant's Nodal Domain Theorem for Positivity Preserving Forms
Matthias Keller, Michael Schwarz
We introduce a notion of nodal domains for positivity preserving forms. This notion generalizes the classical ones for Laplacians on domains and on graphs. We prove the Courant nod…
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…
Criticality theory for Schrödinger operators on graphs
Matthias Keller, Yehuda Pinchover, Felix Pogorzelski
We study Schrödinger operators given by positive quadratic forms on infinite graphs. From there, we develop a criticality theory for Schrödinger operators on general weighted graph…
An improved discrete Hardy inequality
Matthias Keller, Yehuda Pinchover, Felix Pogorzelski
We improve the classical discrete Hardy inequality \begin{equation*}\label{1} \sum _{n=1}^{\infty }a_{n}^{2}\geq \left({\frac {1}{2}}\right)^{2} \sum _{n=1}^{\infty }\left({\frac {…