Title
Gegenbauer polynomials and the Fueter theorem Gegenbauer polynomials and the Fueter theorem
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Publication type
article
Publication
,
Subject
Mathematics
Source (journal)
Complex variables & elliptic equations. - Place of publication unknown
Volume/pages
59(2014) :6 , p. 826-840
ISSN
1747-6933
ISI
000334080400005
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
The Fueter theorem states that regular (resp. monogenic) functions in quaternionic (resp. Clifford) analysis can be constructed from holomorphic functions <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="gcov_a_787531_ilm0001.gif"></inline-graphic> in the complex plane, hereby using a combination of a formal substitution and the action of an appropriate power of the Laplace operator. In this paper we interpret this theorem on the level of representation theory, as an intertwining map between certain <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="gcov_a_787531_ilm0002.gif"></inline-graphic>-modules.
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