COMPLETE ORTHOGONAL SYSTEMS OF 3D SPHEROIDAL MONOGENICS

  • In this paper we review two distint complete orthogonal systems of monogenic polynomials over 3D prolate spheroids. The underlying functions take on either values in the reduced and full quaternions (identified, respectively, with R3 and R4), and are generally assumed to be nullsolutions of the well known Riesz and Moisil Théodoresco systems in R3. This will be done in the spaces of square integrable functions over R and H. The representations of these polynomials are explicitly given. Additionally, we show that these polynomial functions play an important role in defining the Szegö kernel function over the surface of 3D spheroids. As a concrete application, we prove the explicit expression of the monogenic Szegö kernel function over 3D prolate spheroids.

Download full text files

Export metadata

Additional Services

Share in Twitter Search Google Scholar
Metadaten
Document Type:Conference Proceeding
Author: Joao Morais, Svetlin Georgiev
DOI (Cite-Link):https://doi.org/10.25643/bauhaus-universitaet.2778Cite-Link
URN (Cite-Link):https://nbn-resolving.org/urn:nbn:de:gbv:wim2-20170314-27785Cite-Link
URL:http://euklid.bauing.uni-weimar.de/ikm2012
ISSN:1611-4086
Parent Title (English):Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 04 - 06 2012, Bauhaus-University Weimar
Editor: Klaus GürlebeckGND, Tom LahmerORCiDGND, Frank WernerORCiDGND
Language:English
Date of Publication (online):2017/03/03
Date of first Publication:2012/07/04
Release Date:2017/03/14
Publishing Institution:Bauhaus-Universität Weimar
Creating Corporation:Bauhaus-Universität Weimar
Institutes:Bauhaus-Universität Weimar / In Zusammenarbeit mit der Bauhaus-Universität Weimar
Pagenumber:14
GND Keyword:Angewandte Informatik; Angewandte Mathematik; Computerunterstütztes Verfahren
Dewey Decimal Classification:000 Informatik, Informationswissenschaft, allgemeine Werke / 000 Informatik, Wissen, Systeme
500 Naturwissenschaften und Mathematik / 510 Mathematik
BKL-Classification:31 Mathematik / 31.80 Angewandte Mathematik
56 Bauwesen / 56.03 Methoden im Bauingenieurwesen
Collections:Bauhaus-Universität Weimar / Internationales Kolloquium über Anwendungen der Informatik und Mathematik in Architektur und Bauwesen, IKM, Weimar / Internationales Kolloquium über Anwendungen der Informatik und Mathematik in Architektur und Bauwesen, IKM, Weimar, 19. 2012
Licence (German):License Logo Creative Commons 4.0 - Namensnennung-Nicht kommerziell (CC BY-NC 4.0)