Linear Fractional Composition Operators On The Harmonic Dirichlet Space

In this paper we mainly study the adjoint representation and the normality of the linear fractional composition operators on harmonic Dirichlet space, and give the char-acterization for a linear fractional composition operator to be essentially normal.In the first chapter, we introduce some related background and some well-known results on composition operator.In the second chapter, we give some relevant knowledge, some basic concepts and notations.In the third chapter, we study the adjoint representation and the normality of the linear fractional composition operators on harmonic Dirichlet space. Then we put for-ward the sufficient and necessary condition for a linear fractional composition operator to be unitary.In the fourth chapter, we discuss the normality of the linear fractional composition operators on the harmonic Dirichlet space. We also put forward the sufficient and necessary condition for the operator to be normal and the characterization of essentially normal linear fractional composition operator.