@article{CerejeirasKaehlerLegatiuketal.,
  author    = {Cerejeiras, Paula and K{\"a}hler, Uwe and Legatiuk, Anastasiia and Legatiuk, Dmitrii},
  title     = {Discrete Hardy Spaces for Bounded Domains in Rn},
  series = {Complex Analysis and Operator Theory},
  volume    = {2021},
  journal   = {Complex Analysis and Operator Theory},
  number    = {Volume 15, article 4},
  publisher = {Springer},
  address   = {Heidelberg},
  doi       = {10.1007/s11785-020-01047-6},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20210804-44746},
  pages     = {1 -- 32},
  abstract  = {Discrete function theory in higher-dimensional setting has been in active development since many years. However, available results focus on studying discrete setting for such canonical domains as half-space, while the case of bounded domains generally remained unconsidered. Therefore, this paper presents the extension of the higher-dimensional function theory to the case of arbitrary bounded domains in Rn. On this way, discrete Stokes' formula, discrete Borel-Pompeiu formula, as well as discrete Hardy spaces for general bounded domains are constructed. Finally, several discrete Hilbert problems are considered.},
  subject      = {Dirac-Operator},
  language  = {en}
}
@article{LegatiukGuerlebeckHommel,
  author    = {Legatiuk, Anastasiia and G{\"u}rlebeck, Klaus and Hommel, Angela},
  title     = {Estimates for the discrete fundamental solution of the discrete Laplace operator on a rectangular lattice},
  series = {Mathematical Methods in the Applied Sciences},
  volume    = {2021},
  journal   = {Mathematical Methods in the Applied Sciences},
  publisher = {Wiley},
  address   = {Chichester},
  doi       = {10.1002/mma.7747},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20220209-45829},
  pages     = {1 -- 23},
  abstract  = {This paper presents numerical analysis of the discrete fundamental solution of the discrete Laplace operator on a rectangular lattice. Additionally, to provide estimates in interior and exterior domains, two different regularisations of the discrete fundamental solution are considered. Estimates for the absolute difference and lp-estimates are constructed for both regularisations. Thus, this work extends the classical results in the discrete potential theory to the case of a rectangular lattice and serves as a basis for future convergence analysis of the method of discrete potentials on rectangular lattices.},
  subject      = {diskrete Fourier-Transformation},
  language  = {en}
}