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Title: Discrete Hardy spaces for bounded domains in Rn
Other Titles: Discrete Hardy spaces for bounded domains in $${\mathbb {R}}^{n}$$
Author: Cerejeiras, Paula
Kähler, Uwe
Legatiuk, Anastasiia
Legatiuk, Dmitrii
Keywords: Discrete Dirac operator
Discrete monogenic functions
Discrete function theory
Discrete Cauchy transform
Discrete boundary value problems
Issue Date: Feb-2021
Publisher: Springer; Birkhäuser
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 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.
Peer review: yes
DOI: 10.1007/s11785-020-01047-6
ISSN: 1661-8254
Appears in Collections:CIDMA - Artigos
CHAG - Artigos

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