Open AccessSpheroidal Domains and Geometric Analysis in Euclidean Space
Author(s) -
Garret Sobczyk
Publication year - 2021
Publication title -
contemporary mathematics
Language(s) - English
Resource type - Journals
eISSN - 2705-1064
pISSN - 2705-1056
DOI - 10.37256/cm.232021875
Subject(s) - geometric algebra , algebra over a field , mathematics , clifford analysis , multivector , euclidean space , clifford algebra , quaternion , euclidean geometry , cauchy distribution , generalization , pure mathematics , jordan algebra , mathematical analysis , algebra representation , geometry , dirac operator
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.