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TOTALLY REGULAR VARIABLES AND APPELL SEQUENCES IN HYPERCOMPLEX FUNCTION THEORY

  • The aim of our contribution is to clarify the relation between totally regular variables and Appell sequences of hypercomplex holomorphic polynomials (sometimes simply called monogenic power-like functions) in Hypercomplex Function Theory. After their introduction in 2006 by two of the authors of this note on the occasion of the 17th IKM, the latter have been subject of investigations by differentThe aim of our contribution is to clarify the relation between totally regular variables and Appell sequences of hypercomplex holomorphic polynomials (sometimes simply called monogenic power-like functions) in Hypercomplex Function Theory. After their introduction in 2006 by two of the authors of this note on the occasion of the 17th IKM, the latter have been subject of investigations by different authors with different methods and in various contexts. The former concept, introduced by R. Delanghe in 1970 and later also studied by K. Gürlebeck in 1982 for the case of quaternions, has some obvious relationship with the latter, since it describes a set of linear hypercomplex holomorphic functions all power of which are also hypercomplex holomorphic. Due to the non-commutative nature of the underlying Clifford algebra, being totally regular variables or Appell sequences are not trivial properties as it is for the integer powers of the complex variable z=x+ iy. Simple examples show also, that not every totally regular variable and its powers form an Appell sequence and vice versa. Under some very natural normalization condition the set of all para-vector valued totally regular variables which are also Appell sequences will completely be characterized. In some sense the result can also be considered as an answer to a remark of K. Habetha in chapter 16: Function theory in algebras of the collection Complex analysis. Methods, trends, and applications, Akademie-Verlag Berlin, (Eds. E. Lanckau and W. Tutschke) 225-237 (1983) on the use of exact copies of several complex variables for the power series representation of any hypercomplex holomorphic function.show moreshow less

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Metadaten
Document Type:Conference Proceeding
Author: Helmuth R. Malonek, M. Irene Falcão, Carla Cruz
DOI (Cite-Link):https://doi.org/10.25643/bauhaus-universitaet.2775Cite-Link
URN (Cite-Link):https://nbn-resolving.org/urn:nbn:de:gbv:wim2-20170314-27751Cite-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:5
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)