Invertibility And Fredholmness Of The Weighted Composition Operators On Dirichlet Space

The paper studies the invertibility and fredholmness of weighted com-position operators on Dirichlet space , which consists of three chapters.In Chapter I, the research background, some preliminaries and mainresults of the paper are introduced.The Chapter II consists of two sections. In section one,we give somenecessary conditions for weighted composition operators on Dirichlet spaceto be invertible .In section two, the necessary and sufcient conditions forthe invertibility of weighted composition operators on Dirichlet space isobtained.In Chapter III, the necessary and sufcient conditions for the fred-holmness of weighted composition operators on Dirichlet space is obtained.