Abstract

In this thesis we develop vector coherent states (VCS) in the form [Special characters omitted.] where [Special characters omitted.] , the n dimensional complex space and [Special characters omitted.] is an n x n matrix. By imposing some conditions on the matrix [Special characters omitted.] we develop a general procedure to obtain VCS. We develop VCS on the complex plane and on the unit disc by replacing the matrix [Special characters omitted.] by quaternions. We also build VCS with several other classes of matrices. Further, we develop VCS on general Clifford algebras. At last, we build VCS with a class of symmetric matrices with an unbounded frame operator.