On Riemann problems for monogenic functions in lower dimensional non-commutative Clifford algebras

2021 ◽  
Vol 11 (2) ◽  
Author(s):  
Carlos Daniel Tamayo-Castro ◽  
Ricardo Abreu-Blaya ◽  
Juan Bory-Reyes
Keyword(s):  
Clifford Algebras ◽  
Monogenic Functions ◽  
Riemann Problems ◽  
Lower Dimensional

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 About the Dirichlet Boundary Value Problem using Clifford Algebras

2018 ◽  
Vol 15 ◽  
pp. 8098-8119
Author(s):  
Johan Ceballos
Keyword(s):  
Dirichlet Problem ◽  
Boundary Value Problem ◽  
Clifford Algebras ◽  
Dirichlet Boundary ◽  
Relevant Literature ◽  
Monogenic Functions ◽  
Dirichlet Boundary Value Problem ◽  
Dirichlet Problems ◽  
Initial Value ◽  
Do So

This paper reviews and summarizes the relevant literature on Dirichlet problems for monogenic functions on classic Clifford Algebras and the Clifford algebras depending on parameters on. Furthermore, our aim is to explore the properties when extending the problem to and, illustrating it using the concept of fibres. To do so, we explore ways in which the Dirichlet problem can be written in matrix form, using the elements of a Clifford's base. We introduce an algorithm for finding explicit expressions for monogenic functions for Dirichlet problems using matrices in Finally, we illustrate how to solve an initial value problem related to a fibre.

scholarly journals Slice monogenic functions of a Clifford variable via the 𝑆-functional calculus

2021 ◽  
Vol 8 (23) ◽  
pp. 281-296
Author(s):  
Fabrizio Colombo ◽  
David Kimsey ◽  
Stefano Pinton ◽  
Irene Sabadini
Keyword(s):  
Functional Calculus ◽  
Clifford Algebras ◽  
Function Theory ◽  
Monogenic Functions ◽  
Content Type ◽  
New Class ◽  
Zero Divisors ◽  
Slice Monogenic Functions ◽  
Class Of Functions ◽  
Clifford Numbers

In this paper we define a new function theory of slice monogenic functions of a Clifford variable using the S S -functional calculus for Clifford numbers. Previous attempts of such a function theory were obstructed by the fact that Clifford algebras, of sufficiently high order, have zero divisors. The fact that Clifford algebras have zero divisors does not pose any difficulty whatsoever with respect to our approach. The new class of functions introduced in this paper will be called the class of slice monogenic Clifford functions to stress the fact that they are defined on open sets of the Clifford algebra R n \mathbb {R}_n . The methodology can be generalized, for example, to handle the case of noncommuting matrix variables.

Isomorphisms of graded skew Clifford algebras

2020 ◽  
Vol 13 (5) ◽  
pp. 871-878
Author(s):  
Richard G. Chandler ◽  
Nicholas Engel
Keyword(s):  
Clifford Algebras
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