@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{GueneysuKeller2018,
  author    = {G{\"u}neysu, Batu and Keller, Matthias},
  title     = {Scattering the Geometry of Weighted Graphs},
  series = {Mathematical physics, analysis and geometry : an international journal devoted to the theory and applications of analysis and geometry to physics},
  volume    = {21},
  journal   = {Mathematical physics, analysis and geometry : an international journal devoted to the theory and applications of analysis and geometry to physics},
  number    = {3},
  publisher = {Springer},
  address   = {Dordrecht},
  issn      = {1385-0172},
  doi       = {10.1007/s11040-018-9285-1},
  pages     = {15},
  year      = {2018},
  abstract  = {Given two weighted graphs (X, b(k), m(k)), k = 1, 2 with b(1) similar to b(2) and m(1) similar to m(2), we prove a weighted L-1-criterion for the existence and completeness of the wave operators W-+/- (H-2, H-1, I-1,I-2), where H-k denotes the natural Laplacian in l(2)(X, m(k)) w.r.t. (X, b(k), m(k)) and I-1,I-2 the trivial identification of l(2)(X, m(1)) with l(2) (X, m(2)). In particular, this entails a general criterion for the absolutely continuous spectra of H-1 and H-2 to be equal.},
  language  = {en}
}