On convergence propertiesof 3D spheroidal monogenics

Status	已發表Published
	On convergence propertiesof 3D spheroidal monogenics
	Morais, J.; Kou, K. I.; Georgiev, S.
	2013-05-01
Source Publication	International Journal of wavelets multiresolution and information processing
ISSN	0219-6913
Pages	1350024-1-1350024-19
Abstract	J. 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.
Keyword	Quaternion analysis Riesz system Moisil Theodoresco system Ferrer's associated Legendre functions Chebyshev polynomials hyperbolic functions monogenic functions.
Language	英語English
The Source to Article	PB_Publication
PUB ID	9272
Document Type	Journal article
Collection	University of Macau
Corresponding Author	Morais, 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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