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On convergence propertiesof 3D spheroidal monogenics
Morais, J.; Kou, K. I.; Georgiev, S.
2013-05-01
Source PublicationInternational Journal of wavelets multiresolution and information processing
ISSN0219-6913
Pages1350024-1-1350024-19
AbstractJ. Morais 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 R3 and R4, and are generally assumed to be nullsolutions of the well known Riesz and Moisil Theodoresco systems in R3. 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.
KeywordQuaternion analysis Riesz system Moisil Theodoresco system Ferrer's associated Legendre functions Chebyshev polynomials hyperbolic functions monogenic functions.
Language英語English
The Source to ArticlePB_Publication
PUB ID9272
Document TypeJournal article
CollectionUniversity of Macau
Corresponding AuthorMorais, J.
Recommended Citation
GB/T 7714
Morais, J.,Kou, K. I.,Georgiev, S.. On convergence propertiesof 3D spheroidal monogenics[J]. International Journal of wavelets multiresolution and information processing,2013:1350024-1-1350024-19.
APA Morais, J.,Kou, K. I.,&Georgiev, S..(2013).On convergence propertiesof 3D spheroidal monogenics.International Journal of wavelets multiresolution and information processing,1350024-1-1350024-19.
MLA Morais, J.,et al."On convergence propertiesof 3D spheroidal monogenics".International Journal of wavelets multiresolution and information processing (2013):1350024-1-1350024-19.
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