Dirichlet Forms on Canonically Compactifiable Graphs

05.11.2015, 12:30 Uhr  –  Campus Golm, Haus 5, Raum 1.12
Forschungsseminar Diskrete Spektraltheorie

Michael Schwarz (Potsdam)

We consider weighted graphs with an infinite set $X$ of vertices such that every function of finite energy is bounded. For each of these graphs there is a compact set $K$ containing $X$ as a dense subset and, thus, we can define some kind of boundary as $\partial X=K\setminus X$. Then we equip the graph with a finite measure and define two natural Dirichlet forms $Q^{(D)}$ and $Q^{(N)}$. We show that every Dirichlet form $Q$ that satisfies $Q^{(D)}\geq Q\geq Q^{(N)}$ can be decomposed into a part on the graph and a part on the boundary, which is a Dirichlet form (in the wide sense) with respect to a certain measure.