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  • Georgiev, Svetlin (2)
  • Morais, Joao (2)
  • Sprößig, Wolfgang (1)

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  • Computerunterstütztes Verfahren (2)

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COMPLETE ORTHOGONAL SYSTEMS OF 3D SPHEROIDAL MONOGENICS (2012)
Morais, Joao ; Georgiev, Svetlin
In this paper we review two distint complete orthogonal systems of monogenic polynomials over 3D prolate spheroids. 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 Théodoresco systems in R3. This will be done in the spaces of square integrable functions over R and H. The representations of these polynomials are explicitly given. Additionally, we show that these polynomial functions play an important role in defining the Szegö kernel function over the surface of 3D spheroids. As a concrete application, we prove the explicit expression of the monogenic Szegö kernel function over 3D prolate spheroids.
A NOTE ON THE CLIFFORD FOURIER-STIELTJES TRANSFORM (2012)
Morais, Joao ; Georgiev, Svetlin ; Sprößig, Wolfgang
The purpose of this article is to provide an overview of the real Clifford Fourier- Stieltjes transform (CFST) and of its important properties. Additionally, we introduce the definition of convolution of Clifford functions of bounded variation.
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