@article{KellerMuenchPogorzelski2016,
  author    = {Keller, Matthias and M{\"u}nch, Florentin and Pogorzelski, Felix},
  title     = {Geometry and spectrum of rapidly branching graphs},
  series = {Mathematische Nachrichten},
  volume    = {289},
  journal   = {Mathematische Nachrichten},
  publisher = {Wiley-VCH},
  address   = {Weinheim},
  issn      = {0025-584X},
  doi       = {10.1002/mana.201400349},
  pages     = {1636 -- 1647},
  year      = {2016},
  abstract  = {We study graphs whose vertex degree tends to infinity and which are, therefore, called rapidly branching. We prove spectral estimates, discreteness of spectrum, first order eigenvalue and Weyl asymptotics solely in terms of the vertex degree growth. The underlying techniques are estimates on the isoperimetric constant. Furthermore, we give lower volume growth bounds and we provide a new criterion for stochastic incompleteness. (C) 2016 WILEY-VCH Verlag GmbH \& Co. KGaA, Weinheim},
  language  = {en}
}
@article{KellerPinchoverPogorzelski2019,
  author    = {Keller, Matthias and Pinchover, Yehuda and Pogorzelski, Felix},
  title     = {Criticality theory for Schr{\"o}dinger operators on graphs},
  series = {Journal of spectral theory},
  volume    = {10},
  journal   = {Journal of spectral theory},
  number    = {1},
  publisher = {European Mathematical Society},
  address   = {Z{\"u}rich},
  issn      = {1664-039X},
  doi       = {10.4171/JST/286},
  pages     = {73 -- 114},
  year      = {2019},
  abstract  = {We study Schrodinger operators given by positive quadratic forms on infinite graphs. From there, we develop a criticality theory for Schrodinger operators on general weighted graphs.},
  language  = {en}
}
@article{KellerPinchoverPogorzelski2018,
  author    = {Keller, Matthias and Pinchover, Yehuda and Pogorzelski, Felix},
  title     = {Optimal Hardy inequalities for Schrodinger operators on graphs},
  series = {Communications in mathematical physics},
  volume    = {358},
  journal   = {Communications in mathematical physics},
  number    = {2},
  publisher = {Springer},
  address   = {New York},
  issn      = {0010-3616},
  doi       = {10.1007/s00220-018-3107-y},
  pages     = {767 -- 790},
  year      = {2018},
  abstract  = {For a given subcritical discrete Schrodinger operator H on a weighted infinite graph X, we construct a Hardy-weight w which is optimal in the following sense. The operator H - lambda w is subcritical in X for all lambda < 1, null-critical in X for lambda = 1, and supercritical near any neighborhood of infinity in X for any lambda > 1. Our results rely on a criticality theory for Schrodinger operators on general weighted graphs.},
  language  = {en}
}
@article{KellerPinchoverPogorzelski2018,
  author    = {Keller, Matthias and Pinchover, Yehuda and Pogorzelski, Felix},
  title     = {An improved discrete hardy inequality},
  series = {The American mathematical monthly : an official publication of the Mathematical Association of America},
  volume    = {125},
  journal   = {The American mathematical monthly : an official publication of the Mathematical Association of America},
  number    = {4},
  publisher = {Taylor \& Francis Group},
  address   = {Philadelphia},
  issn      = {0002-9890},
  doi       = {10.1080/00029890.2018.1420995},
  pages     = {347 -- 350},
  year      = {2018},
  abstract  = {In this note, we prove an improvement of the classical discrete Hardy inequality. Our improved Hardy-type inequality holds with a weight w which is strictly greater than the classical Hardy weight w(H)(n) : 1/(2n)(2), where N.},
  language  = {en}
}
@article{KellerPinchoverPogorzelski2020,
  author    = {Keller, Matthias and Pinchover, Yehuda and Pogorzelski, Felix},
  title     = {From hardy to rellich inequalities on graphs},
  series = {Proceedings of the London Mathematical Society},
  volume    = {122},
  journal   = {Proceedings of the London Mathematical Society},
  number    = {3},
  publisher = {Wiley},
  address   = {Hoboken},
  issn      = {0024-6115},
  doi       = {10.1112/plms.12376},
  pages     = {458 -- 477},
  year      = {2020},
  abstract  = {We show how to deduce Rellich inequalities from Hardy inequalities on infinite graphs. Specifically, the obtained Rellich inequality gives an upper bound on a function by the Laplacian of the function in terms of weighted norms. These weights involve the Hardy weight and a function which satisfies an eikonal inequality. The results are proven first for Laplacians and are extended to Schrodinger operators afterwards.},
  language  = {en}
}
@misc{KellerPinchoverPogorzelski2020,
  author    = {Keller, Matthias and Pinchover, Yehuda and Pogorzelski, Felix},
  title     = {From hardy to rellich inequalities on graphs},
  series = {Zweitver{\"o}ffentlichungen der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  journal   = {Zweitver{\"o}ffentlichungen der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  number    = {3},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-54214},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-542140},
  pages     = {22},
  year      = {2020},
  abstract  = {We show how to deduce Rellich inequalities from Hardy inequalities on infinite graphs. Specifically, the obtained Rellich inequality gives an upper bound on a function by the Laplacian of the function in terms of weighted norms. These weights involve the Hardy weight and a function which satisfies an eikonal inequality. The results are proven first for Laplacians and are extended to Schrodinger operators afterwards.},
  language  = {en}
}