Formalizing Basic Quaternionic Analysis

2017 ◽  
pp. 225-240 ◽  
Author(s):  
Andrea Gabrielli ◽  
Marco Maggesi
Keyword(s):  
Quaternionic Analysis

Slice quaternionic analysis in two variables

2021 ◽  
pp. 1-24
Author(s):  
Xinyuan Dou ◽  
Guangbin Ren ◽  
Irene Sabadini ◽  
Xieping Wang
Keyword(s):  
Quaternionic Analysis

Dirichlet-Type Problems for the Two-Dimensional Helmholtz Operator in Complex Quaternionic Analysis

2016 ◽  
Vol 13 (6) ◽  
pp. 4901-4916 ◽  
Author(s):  
Juan Bory-Reyes ◽  
Ricardo Abreu-Blaya ◽  
Luis M. Hernández-Simon ◽  
Baruch Schneider
Keyword(s):  
Quaternionic Analysis ◽  
Two Dimensional ◽  
Helmholtz Operator ◽  
Dirichlet Type

Modified Quaternionic Analysis in R[sup 3] and Generalizations of Conformal Mappings of the Second Kind

2011 ◽  
Author(s):  
Dmitry Bryukhov ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras ◽  
Zacharias Anastassi
Keyword(s):  
Conformal Mappings ◽  
Quaternionic Analysis ◽  
Modified Quaternionic Analysis

scholarly journals Quaternionic analysis, representation theory and physics

2008 ◽  
Vol 218 (6) ◽  
pp. 1806-1877 ◽  
Author(s):  
Igor Frenkel ◽  
Matvei Libine
Keyword(s):  
Representation Theory ◽  
Quaternionic Analysis

Quaternionic analysis

1979 ◽  
Vol 85 (2) ◽  
pp. 199-225 ◽  
Author(s):  
A. Sudbery
Keyword(s):  
Division Algebra ◽  
Complex Variable ◽  
Special Class ◽  
Quaternionic Analysis ◽  
Complex Field ◽  
Regular Functions ◽  
Basic Ideas ◽  
Similar Theory ◽  
First Time ◽  
Modern Form

The richness of the theory of functions over the complex field makes it natural to look for a similar theory for the only other non-trivial real associative division algebra, namely the quaternions. Such a theory exists and is quite far-reaching, yet it seems to be little known. It was not developed until nearly a century after Hamilton's discovery of quaternions. Hamilton himself (1) and his principal followers and expositors, Tait(2) and Joly(3), only developed the theory of functions of a quaternion variable as far as it could be taken by the general methods of the theory of functions of several real variables (the basic ideas of which appeared in their modern form for the first time in Hamilton's work on quaternions). They did not delimit a special class of regular functions among quaternion-valued functions of a quaternion variable, analogous to the regular functions of a complex variable.

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