Eigenfunctions growth of R-limits on graphs
Siegfried Beckus
University of Potsdam, GermanyLatif Eliaz
Technion Israel Institute of Technology, Haifa, Israel
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Abstract
A characterization of the essential spectrum of Schrödinger operators on infinite graphs is derived involving the concept of -limits. This concept, which was introduced previously for operators on and as “right-limits,” captures the behaviour of the operator at infinity. For graphs with sub-exponential growth rate, we show that each point in corresponds to a bounded generalized eigenfunction of a corresponding -limit of . If, additionally, the graph is of uniform sub-exponential growth, also the converse inclusion holds.
Cite this article
Siegfried Beckus, Latif Eliaz, Eigenfunctions growth of R-limits on graphs. J. Spectr. Theory 11 (2021), no. 4, pp. 1895–1933
DOI 10.4171/JST/389