Study Of Multiplication Operators On Bergman Space

Bergman space is a space of analytic functions that are squared integrable over a region.Duality theorem is an important conclusion to Bergman space,which comes in many forms generalization,the study of various operators on these spaces is the feld of functional analysis frontier hot issues.This paper employs Cowen-Douglas operator theory to prove that on any simply connected region in the complex plane C,the Bergman space multiplication operator with the M?bius transformation as its multiplier is a forward shift operator on some Markushevich basis.