@article{BeckusEliaz2021,
  author    = {Beckus, Siegfried and Eliaz, Latif},
  title     = {Eigenfunctions growth of R-limits on graphs},
  series = {Journal of spectral theory / European Mathematical Society},
  volume    = {11},
  journal   = {Journal of spectral theory / European Mathematical Society},
  number    = {4},
  publisher = {EMS Press, an imprint of the European Mathematical Society - EMS - Publishing House GmbH, Institut f{\"u}r Mathematik, Technische Universit{\"a}t},
  address   = {Berlin},
  issn      = {1664-039X},
  doi       = {10.4171/JST/389},
  pages     = {1895 -- 1933},
  year      = {2021},
  abstract  = {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.},
  language  = {en}
}