TY: JOUR
T1 - Discrete Hardy spaces for bounded domains in Rn
A1 - Cerejeiras, Paula
A1 - Kähler, Uwe
A1 - Legatiuk, Anastasiia
A1 - Legatiuk, Dmitrii
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 R^n. 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.
UR - https://ria.ua.pt/handle/10773/29892
Y1 - 2021
PB - Springer; Birkhäuser