Add to ORKGThe theory of mathematical analysis over split quaternions is formulated in a closest possible analogy to the usual theory of analytic functions of a complex variable. After reviewing split quaternion algebra via an isomorphic 4 £ 4 matrix representation, a different definition is given to partial derivatives involving split quaternions. This takes care of the ambiguity involved in the no commutative properties of split quaternions. A closely analogous condition for analyticity of functions of a split quaternion variable is found. The analogy with complex variables is illustrated for both the derivative.128-13
It is well known that a general quaternion algebra over a field F of characteristic different from 2...
The algebra of split quaternions is a recently increasing topic in the study of theory and numerical...
The regularity of a quaternionic function is reinterpreted through a new canonical decomposition of ...
In this thesis, we study Quaternionic Analysis, which is the most natural and close generalization o...
This paper aims to present, in a unified manner, results which are valid on both split quaternions w...
Many properties of complex functions are pretty difficult to be generalized in the field of quaterni...
AbstractWe investigate differentiability of functions defined on regions of the real quaternion fiel...
Quaternionic Clifford analysis is a recent new branch of Clifford analysis, a higher dimensional fun...
Notions of a “holomorphic ” function theory for functions of a split-quaternionic variable have been...
Alesker studied a relation between the determinant of a quaternionic Hessian of a function and a spe...
In this paper, we introduce the concept of consimilarity of split quaternions and split quaternion m...
Most of theoretical physics is based on the mathematics of functions of a real or a complex variable...
In this study, we introduce the concept of semisimilarity and consemisimilarity of split quaternions...
Recent innovations in the differential calculus for functions of non-commuting variables, begun for...
The step derivative of a complex function can be defined with various methods. The step direction de...
It is well known that a general quaternion algebra over a field F of characteristic different from 2...
The algebra of split quaternions is a recently increasing topic in the study of theory and numerical...
The regularity of a quaternionic function is reinterpreted through a new canonical decomposition of ...
In this thesis, we study Quaternionic Analysis, which is the most natural and close generalization o...
This paper aims to present, in a unified manner, results which are valid on both split quaternions w...
Many properties of complex functions are pretty difficult to be generalized in the field of quaterni...
AbstractWe investigate differentiability of functions defined on regions of the real quaternion fiel...
Quaternionic Clifford analysis is a recent new branch of Clifford analysis, a higher dimensional fun...
Notions of a “holomorphic ” function theory for functions of a split-quaternionic variable have been...
Alesker studied a relation between the determinant of a quaternionic Hessian of a function and a spe...
In this paper, we introduce the concept of consimilarity of split quaternions and split quaternion m...
Most of theoretical physics is based on the mathematics of functions of a real or a complex variable...
In this study, we introduce the concept of semisimilarity and consemisimilarity of split quaternions...
Recent innovations in the differential calculus for functions of non-commuting variables, begun for...
The step derivative of a complex function can be defined with various methods. The step direction de...
It is well known that a general quaternion algebra over a field F of characteristic different from 2...
The algebra of split quaternions is a recently increasing topic in the study of theory and numerical...
The regularity of a quaternionic function is reinterpreted through a new canonical decomposition of ...