The Relevant Characterization Of Composition Operators On Function Space

This thesis studies the Toeplitzness, Hankelness and complex conju-gate symmetric property relating to composition operators on the Hardy space, Bergman space, Dirichlet space. Their are four parts in this paper.In part1, we introduce the related research background and research status and state the main results in the paper.In part2, We give the basic knowledge of the unit circle D on the Hardy space H2, proving the Hankelness and complex conjugta symmetric property of C*φC*φ and Cφ1Cφ2on H2.In part3, We give the basic knowledge of the unit disk D on the Bergman space L2a,proving the similar Toeplitzness and similar Hankelness on L2aIn part4, We give the basic knowledge of the unit disk D on the Dirichlet space D, proving the complex conjugate symmetric property of W(?) on D...