TY  - JOUR
A1  - Legatiuk, Anastasiia
A1  - Gürlebeck, Klaus
A1  - Hommel, Angela
T1  - Estimates for the discrete fundamental solution of the discrete Laplace operator on a rectangular lattice
JF  - Mathematical Methods in the Applied Sciences
N2  - 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.
KW  - diskrete Fourier-Transformation
KW  - Laplace-Operator
KW  - discrete fourier transform
KW  - discrete fundamental solution
KW  - laplace operator
KW  - rectangular lattice
Y1  - 2021
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20220209-45829
UR  - https://onlinelibrary.wiley.com/doi/full/10.1002/mma.7747
VL  - 2021
SP  - 1
EP  - 23
PB  - Wiley
CY  - Chichester
ER  - 
TY  - JOUR
A1  - Cerejeiras, Paula
A1  - Kähler, Uwe
A1  - Legatiuk, Anastasiia
A1  - Legatiuk, Dmitrii
T1  - Discrete Hardy Spaces for Bounded Domains in Rn
JF  - Complex Analysis and Operator Theory
N2  - 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.
KW  - Dirac-Operator
KW  - Randwertproblem
KW  - Funktionentheorie
KW  - discrete Dirac operator
KW  - discrete monogenic functions
KW  - discrete boundary value problems
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20210804-44746
UR  - https://link.springer.com/article/10.1007/s11785-020-01047-6
VL  - 2021
IS  - Volume 15, article 4
SP  - 1
EP  - 32
PB  - Springer
CY  - Heidelberg
ER  -