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On 3D orthogonal prolate spheroidal monogenics
Morais J.1; Nguyen H.M.3; Kou K.I.2
Source PublicationMathematical Methods in the Applied Sciences
ISSN10991476 01704214

S. G. Georgiev, Complete orthogonal systems of monogenic polynomials over 3D prolate spheroids have recently experienced an upsurge of interest because of their many remarkable properties. These generalized polynomials and their applications to the theory of quasi-conformal mappings and approximation theory have played a major role in this development. In particular, the underlying functions of three real variables take on values in the reduced quaternions (identified with) and are generally assumed to be null-solutions of the well-known Riesz system in. The present paper introduces and explores a new complete orthogonal system of monogenic functions as solutions to this system for the space exterior of a 3D prolate spheroid. This will be made in the linear spaces of square integrable functions over. The representations of these functions are explicitly given. Some important properties of the system are briefly discussed, from which several recurrence formulae for fast computer implementations can be derived.

KeywordFerrer's Associated Legendre Functions Hyperbolic Functions Prolate Spheroidal Harmonics Prolate Spheroidal Monogenics Quaternionic Analysis Riesz System
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Indexed BySCIE
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000370234600002
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Cited Times [WOS]:3   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
Affiliation1.Instituto Tecnológico Autonómo de México
2.Universidade de Macau
3.Bauhaus-Universität Weimar
Recommended Citation
GB/T 7714
Morais J.,Nguyen H.M.,Kou K.I.. On 3D orthogonal prolate spheroidal monogenics[J]. Mathematical Methods in the Applied Sciences,2016,39(4):635-648.
APA Morais J.,Nguyen H.M.,&Kou K.I..(2016).On 3D orthogonal prolate spheroidal monogenics.Mathematical Methods in the Applied Sciences,39(4),635-648.
MLA Morais J.,et al."On 3D orthogonal prolate spheroidal monogenics".Mathematical Methods in the Applied Sciences 39.4(2016):635-648.
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