Definition 3
The class of
![$\mathbb {T}$](img77.gif)
-holomorphic mappings on a open set
![$U\subseteq\mathbb {C}^{2}$](img78.gif)
is
defined as follows:
It is the subclass of holomorphic mappings of
![$\mathbb {C}^{2}$](img2.gif)
satisfying the complexified
Cauchy-Riemann equations.
Theorem 4
If
![$f_{e1}:X_1\longrightarrow \mathbb {C}_{1}$](img95.gif)
and
![$f_{e2}:X_1\longrightarrow \mathbb {C}_{1}$](img96.gif)
are holomorphic functions of
![$\mathbb {C}_{1}$](img54.gif)
on the domains
![$X_1$](img91.gif)
and
![$X_2$](img92.gif)
respectively,
then the function
![$f:X_1\times_e X_2\longrightarrow \mathbb {C}_{2}$](img97.gif)
defined as
is
![$\mathbb {C}_{2}$](img48.gif)
-holomorphic on the domain