@article{PetreskadeCastroSandevetal.2020,
  author    = {Petreska, Irina and de Castro, Antonio S. M. and Sandev, Trifce and Lenzi, Ervin K.},
  title     = {The time-dependent Schr{\"o}dinger equation in non-integer dimensions for constrained quantum motion},
  series = {Modern physics letters : A, Particles and fields, gravitation, cosmology, nuclear physics},
  volume    = {384},
  journal   = {Modern physics letters : A, Particles and fields, gravitation, cosmology, nuclear physics},
  number    = {34},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {0375-9601},
  doi       = {10.1016/j.physleta.2020.126866},
  pages     = {9},
  year      = {2020},
  abstract  = {We propose a theoretical model, based on a generalized Schroedinger equation, to study the behavior of a constrained quantum system in non-integer, lower than two-dimensional space. The non-integer dimensional space is formed as a product space X x Y, comprising x-coordinate with a Hausdorff measure of dimension alpha(1) = D -1 (1 < D < 2) and y-coordinate with the Lebesgue measure of dimension of length (alpha(2) = 1). Geometric constraints are set at y = 0. Two different approaches to find the Green's function are employed, both giving the same form in terms of the Fox H-function. For D = 2, the solution for two-dimensional quantum motion on a comb is recovered. (C) 2020 Elsevier B.V. All rights reserved.},
  language  = {en}
}
@article{FischerKeller2021,
  author    = {Fischer, Florian and Keller, Matthias},
  title     = {Riesz decompositions for Schr{\"o}dinger operators on graphs},
  series = {Journal of mathematical analysis and applications},
  volume    = {495},
  journal   = {Journal of mathematical analysis and applications},
  number    = {1},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {0022-247X},
  doi       = {10.1016/j.jmaa.2020.124674},
  pages     = {22},
  year      = {2021},
  abstract  = {We study superharmonic functions for Schrodinger operators on general weighted graphs. Specifically, we prove two decompositions which both go under the name Riesz decomposition in the literature. The first one decomposes a superharmonic function into a harmonic and a potential part. The second one decomposes a superharmonic function into a sum of superharmonic functions with certain upper bounds given by prescribed superharmonic functions. As application we show a Brelot type theorem.},
  language  = {en}
}