Vector Coherent States with an Unbounded Inverse Frame Operator

We present a class of vector coherent states in the domain $D\times D\times >....\times D$ (n-copies), where $D$ is the complex unit disc, using a specific class of hermitian matrices. Further, as an example, we build vector coherent states in the unit disc by considering the unit disc as the homogeneous space of the group SU(1,1).