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http://hdl.handle.net/10773/29892
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 |
URI: | http://hdl.handle.net/10773/29892 |
DOI: | 10.1007/s11785-020-01047-6 |
ISSN: | 1661-8254 |
Appears in Collections: | CIDMA - Artigos CHAG - Artigos |
Files in This Item:
File | Description | Size | Format | |
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Cerejeiras2020_Article_DiscreteHardySpacesForBoundedD.pdf | 414.24 kB | Adobe PDF | View/Open |
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