First Order Differential Operators Associated to the Space of Monogenic Functions in Parameter-Depending Clifford Algebras

2015 ◽  
Vol 26 (1) ◽  
pp. 13-29 ◽  
Author(s):  
Eusebio Ariza ◽  
Judith Vanegas ◽  
Franklin Vargas
Keyword(s):  
Clifford Algebras ◽  
Differential Operators ◽  
Monogenic Functions ◽  
First Order

First Order Differential Operators Associated to the Space of q-Monogenic Functions

2015 ◽  
Vol 27 (1) ◽  
pp. 135-147
Author(s):  
Eusebio Ariza García ◽  
Antonio Di Teodoro ◽  
Judith Vanegas
Keyword(s):  
Differential Operators ◽  
Monogenic Functions ◽  
First Order

Series expansions for monogenic functions in Clifford algebras and their application

2020 ◽  
Vol 17 (3) ◽  
pp. 365-371
Author(s):  
Anatoliy Pogorui ◽  
Tamila Kolomiiets
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Vector Space ◽  
Clifford Algebra ◽  
Clifford Algebras ◽  
Monogenic Function ◽  
Second Order ◽  
Series Expansions ◽  
Monogenic Functions ◽  
Partial Differential

This paper deals with studying some properties of a monogenic function defined on a vector space with values in the Clifford algebra generated by the space. We provide some expansions of a monogenic function and consider its application to study solutions of second-order partial differential equations.

scholarly journals On Certain Proximities and Preorderings on the Transposition Hypergroups of Linear First-Order Partial Differential Operators

2014 ◽  
Vol 22 (1) ◽  
pp. 85-103 ◽  
Author(s):  
Jan Chvalina ◽  
Šárka Hošková-Mayerová
Keyword(s):  
Differential Operators ◽  
Partial Differential ◽  
First Order ◽  
Ordered Groups ◽  
Partial Differential Operators ◽  
Power Set

AbstractThe contribution aims to create hypergroups of linear first-order partial differential operators with proximities, one of which creates a tolerance semigroup on the power set of the mentioned differential operators. Constructions of investigated hypergroups are based on the so called “Ends-Lemma” applied on ordered groups of differnetial operators. Moreover, there is also obtained a regularly preordered transpositions hypergroup of considered partial differntial operators.

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