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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.show moreshow less

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Metadaten
Document Type:Article
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):License Logo Creative Commons 4.0 - Namensnennung (CC BY 4.0)