@article{HinzSchwarz2022,
  author    = {Hinz, Michael and Schwarz, Michael},
  title     = {A note on Neumann problems on graphs},
  series = {Positivity},
  volume    = {26},
  journal   = {Positivity},
  number    = {4},
  publisher = {Springer},
  address   = {Dordrecht},
  issn      = {1385-1292},
  doi       = {10.1007/s11117-022-00930-0},
  pages     = {23},
  year      = {2022},
  abstract  = {We discuss Neumann problems for self-adjoint Laplacians on (possibly infinite) graphs. Under the assumption that the heat semigroup is ultracontractive we discuss the unique solvability for non-empty subgraphs with respect to the vertex boundary and provide analytic and probabilistic representations for Neumann solutions. A second result deals with Neumann problems on canonically compactifiable graphs with respect to the Royden boundary and provides conditions for unique solvability and analytic and probabilistic representations.},
  language  = {en}
}
@article{KellerLenzSchmidtetal.2019,
  author    = {Keller, Matthias and Lenz, Daniel and Schmidt, Marcel and Schwarz, Michael},
  title     = {Boundary representation of Dirichlet forms on discrete spaces},
  series = {Journal de Math{\´e}matiques Pures et Appliqu{\´e}es},
  volume    = {126},
  journal   = {Journal de Math{\´e}matiques Pures et Appliqu{\´e}es},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {0021-7824},
  doi       = {10.1016/j.matpur.2018.10.005},
  pages     = {109 -- 143},
  year      = {2019},
  abstract  = {We describe the set of all Dirichlet forms associated to a given infinite graph in terms of Dirichlet forms on its Royden boundary. Our approach is purely analytical and uses form methods. (C) 2018 Elsevier Masson SAS.},
  language  = {en}
}