27 citations · 166 across the 39 of their papers we have counts for
4 papers · 1 filter
On the spectrum of Laplacians on graphs
Frank Bauer, Bobo Hua, Matthias Keller
We study the -independence of spectra of Laplace operators on graphs arising from regular Dirichlet forms on discrete spaces. Here, a sufficient criterion is given solely by a u…
Cheeger inequalities for unbounded graph Laplacians
Frank Bauer, Matthias Keller, Radosław K. Wojciechowski
We use the concept of intrinsic metrics to give a new definition for an isoperimetric constant of a graph. We use this novel isoperimetric constant to prove a Cheeger-type estimate…
A note on self-adjoint extensions of the Laplacian on weighted graphs
Xueping Huang, Matthias Keller, Jun Masamune +1
We study the uniqueness of self-adjoint and Markovian extensions of the Laplacian on weighted graphs. We first show that, for locally finite graphs and a certain family of metrics,…
Volume growth and bounds for the essential spectrum for Dirichlet forms
Sebastian Haeseler, Matthias Keller, Radosław K. Wojciechowski
We consider operators arising from regular Dirichlet forms with vanishing killing term. We give bounds for the bottom of the (essential) spectrum in terms of exponential volume gro…