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Discrete Hardy Spaces for Bounded Domains in Rn
- 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 boundedDiscrete 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.…
Document Type: | Article |
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Author: | Paula CerejeirasGND, Uwe KählerGND, Anastasiia LegatiukORCiD, Dr. Dmitrii LegatiukORCiDGND |
DOI (Cite-Link): | https://doi.org/10.1007/s11785-020-01047-6Cite-Link |
URN (Cite-Link): | https://nbn-resolving.org/urn:nbn:de:gbv:wim2-20210804-44746Cite-Link |
URL: | https://link.springer.com/article/10.1007/s11785-020-01047-6 |
Parent Title (English): | Complex Analysis and Operator Theory |
Publisher: | Springer |
Place of publication: | Heidelberg |
Language: | English |
Date of Publication (online): | 2021/08/02 |
Date of first Publication: | 2020/11/02 |
Release Date: | 2021/08/04 |
Publishing Institution: | Bauhaus-Universität Weimar |
Institutes and partner institutions: | Fakultät Bauingenieurwesen / Professur Angewandte Mathematik |
Volume: | 2021 |
Issue: | Volume 15, article 4 |
Pagenumber: | 32 |
First Page: | 1 |
Last Page: | 32 |
Tag: | discrete Dirac operator; discrete boundary value problems; discrete monogenic functions |
GND Keyword: | Dirac-Operator; Randwertproblem; Funktionentheorie |
Dewey Decimal Classification: | 600 Technik, Medizin, angewandte Wissenschaften / 620 Ingenieurwissenschaften |
BKL-Classification: | 31 Mathematik / 31.47 Operatortheorie |
Licence (German): | Creative Commons 4.0 - Namensnennung (CC BY 4.0) |