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Journal of Spectral Theory

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Volume 10, Issue 1, 2020, pp. 73–114
DOI: 10.4171/JST/286

Published online: 2019-09-16

Criticality theory for Schrödinger operators on graphs

Matthias Keller[1], Yehuda Pinchover[2] and Felix Pogorzelski[3]

(1) Universität Potsdam, Germany
(2) Technion – Israel Institute of Technology, Haifa, Israel
(3) Universität Leipzig, Germany

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 graphs.

Keywords: Green function, ground state, positive solutions, discrete Schrödinger operators, weighted graphs

Keller Matthias, Pinchover Yehuda, Pogorzelski Felix: Criticality theory for Schrödinger operators on graphs. J. Spectr. Theory 10 (2020), 73-114. doi: 10.4171/JST/286