ABSTRACT
The well-known Riemann mapping theorem asserts that every simply connected planar domain with at least two boundary points can be conformally mapped onto the unit disc by a holomorphic mapping. However similar situation does not hold in the case of several complex variables. Bergman introduced two important types of such canonical domains, that is, the minimal domain and the representative domain by using his kernel function. This chapter considers representative domain in matrix space. Using results of vector valued function and properties of matrix, matrix valued representative function of matrix domain with certain conditions are obtained. The chapter discusses preliminary and representative matrix valued function. It describes theorems related to preliminary and representative matrix valued function.
