TY  - JOUR
A1  - Beckus, Siegfried
A1  - Eliaz, Latif
T1  - Eigenfunctions growth of R-limits on graphs
JF  - Journal of spectral theory / European Mathematical Society
N2  - A characterization of the essential spectrum of Schrodinger operators on infinite graphs is derived involving the concept of R-limits. This concept, which was introduced previously for operators on N and Z(d) as "right-limits," captures the behaviour of the operator at infinity. For graphs with sub-exponential growth rate, we show that each point in sigma(ss)(H) corresponds to a bounded generalized eigenfunction of a corresponding R-limit of H. If, additionally, the graph is of uniform sub-exponential growth, also the converse inclusion holds.
KW  - Essential spectrum
KW  - Schrodinger operators
KW  - graphs
KW  - right limits
KW  - generalized eigenfunctions
Y1  - 2021
U6  - https://doi.org/10.4171/JST/389
SN  - 1664-039X
SN  - 1664-0403
VL  - 11
IS  - 4
SP  - 1895
EP  - 1933
PB  - EMS Press, an imprint of the European Mathematical Society - EMS - Publishing House GmbH, Institut für Mathematik, Technische Universität
CY  - Berlin
ER  -