Semi Groupes et Op´erateurs de Toeplitz

Abstract

This thesis is interested in the product and commutativity problems of quasihomogeneous Toeplitz operators which remains an open problem until today. Many encouraging results in this topic are discussed. This done, seeing that the notions of power and root play a very important role in the study of the commutativity of these operators. Then, we present our contribution on the power of these operators in a particular case. Secondly, we carry out a study on the Toeplitz operators defined on the Hardy space. Precisely, the operators in the Model space which are called the truncated Toeplitz operators. The work on the theme of the semi-groups of Toeplitz operators on the Model space is introduced.