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On convergence properties of 3D spheroidal monogenics
Morais,J.1; Kou,K. I.2; Georgiev,S.3
2013
Source PublicationInternational Journal of Wavelets, Multiresolution and Information Processing
ISSN0219-6913
Volume11Issue:3
AbstractMorais has recently introduced certain complete orthogonal sets of monogenic polynomials over 3D prolate spheroids with remarkable properties. The underlying functions take on either values in the reduced and full quaternions (identified, respectively, with R and R), and are generally assumed to be nullsolutions of the well known Riesz and Moisil-Théodoresco systems in R. In continuation of these studies, we recall some fundamental properties of the polynomials, and prove some recursive formulae between them. As a consequence, we obtain a two-term type recurrence relation satisfied by those basis polynomials. These results are then employed to investigate a rather wide class of approximation properties for monogenic functions over 3D prolate spheroids in terms of spheroidal monogenics. © 2013 World Scientific Publishing Company.
KeywordChebyshev polynomials Ferrer's associated Legendre functions hyperbolic functions Moisil-Théodoresco system monogenic functions Quaternion analysis Riesz system
DOI10.1142/S0219691313500240
URLView the original
Language英語English
Scopus ID2-s2.0-84878946960
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Cited Times [WOS]:7   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionUniversity of Macau
Affiliation1.Centro de Investigação e Desenvolvimento em Matemática e Aplicações,Universidade de Aveiro,3810-193 Aveiro,Portugal
2.Faculty of Science and Technology,University of Macau,Macao
3.Department of Differential Equations,University of Sofia,Sofia,Bulgaria
Recommended Citation
GB/T 7714
Morais,J.,Kou,K. I.,Georgiev,S.. On convergence properties of 3D spheroidal monogenics[J]. International Journal of Wavelets, Multiresolution and Information Processing,2013,11(3).
APA Morais,J.,Kou,K. I.,&Georgiev,S..(2013).On convergence properties of 3D spheroidal monogenics.International Journal of Wavelets, Multiresolution and Information Processing,11(3).
MLA Morais,J.,et al."On convergence properties of 3D spheroidal monogenics".International Journal of Wavelets, Multiresolution and Information Processing 11.3(2013).
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