Spheroidal Domains and Geometric Analysis in Euclidean Space

Authors

  • Garret Sobczyk Department of Actuara, Physics and Mathematics, University of the Americas, 72820 Puebla, Pue., Mexico

DOI:

https://doi.org/10.37256/cm.232021875

Keywords:

geometric analysis, Clifford analysis, Spheroidal Laplacians, quasi-monogenic functions

Abstract

Clifford's geometric algebra has enjoyed phenomenal development over the last 60 years by mathematicians, theoretical physicists, engineers, and computer scientists in robotics, artificial intelligence and data analysis, introducing a myriad of different and often confusing notations. The geometric algebra of Euclidean 3-space, the natural generalization of both the well-known Gibbs-Heaviside vector algebra and Hamilton's quaternions, is used here to study spheroidal domains, spheroidal-graphic projections, the Laplace equation, and its Lie algebra of symmetries. The Cauchy-Kovalevska extension and the Cauchy kernel function are treated in a unified way. The concept of a quasi-monogenic family of functions is introduced and studied. 

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Published

2021-06-25

How to Cite

1.
Sobczyk G. Spheroidal Domains and Geometric Analysis in Euclidean Space. Contemp. Math. [Internet]. 2021 Jun. 25 [cited 2024 May 27];2(3):189-20. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/875