Kuzmenko T. Monogenic mappings in the algebra of complex quaternions

The principal algebraic-analytic properties of G-monogenic mappings taking values in the algebra H(C) are investigated in PhD thesis. We have obtained constructive descriptions of all G-monogenic mappings by means of four corresponding analytic functions of complex variable. Analogues of the Cauchy integral theorems for both a surface integral and a curvilinear integral of G-monogenic mappings as well as analogues of the Cauchy integral formula are proved for these mappings. Analogues of the Morera theorem, the Taylor theorem and the Laurent theorem for G-monogenic mappings taking values in the algebra H(C) are also proved. The principal algebraic-analytic properties of H-monogenic mappings taking values in the algebra H(C) are investigated. The relation between G-monogenic and H-monogenic mappings is established and a theorem about the equivalence of different definitions of right-G-monogenic and left-G-monogenic mappings is proved.