Extension Theorems for Monogenic Functions with Parameter Taking Values in a Clifford Algebra

2000 ◽  
pp. 1459-1469
Author(s):  
Hung Le Son
Keyword(s):  
Clifford Algebra ◽  
Monogenic Functions ◽  
Extension Theorems

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 Szegő projections for hardy spaces of monogenic functions and applications

2002 ◽  
Vol 29 (10) ◽  
pp. 613-624 ◽  
Author(s):  
Swanhild Bernstein ◽  
Loredana Lanzani
Keyword(s):  
Dirichlet Problem ◽  
Clifford Algebra ◽  
Bounded Domain ◽  
Hardy Spaces ◽  
Explicit Representation ◽  
Monogenic Functions ◽  
Orthogonal Decompositions

We introduce Szegő projections for Hardy spaces of monogenic functions defined on a bounded domainΩinℝn. We use such projections to obtain explicit orthogonal decompositions forL2(bΩ). As an application, we obtain an explicit representation of the solution of the Dirichlet problem for balls and half spaces withL2, Clifford algebra-valued, boundary datum.

Friedrichs type extension theorems for multivalued operators

1991 ◽  
Vol 2 (1) ◽  
pp. 105-121
Author(s):  
George Dinca ◽  
Daniel Mateescu
Keyword(s):  
Extension Theorems ◽  
Multivalued Operators

scholarly journals On the generalized order and generalized type of entire monogenic functions

2013 ◽  
Vol 46 (4) ◽  
Author(s):  
G. S. Srivastava ◽  
Susheel Kumar
Keyword(s):  
Lower Order ◽  
Monogenic Functions ◽  
Generalized Type ◽  
Taylor’S Series ◽  
Generalized Order

AbstractIn the present paper we study the generalized growth of entire monogenic functions. The generalized order, generalized lower order and generalized type of entire monogenic functions have been obtained in terms of its Taylor’s series coefficients.

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