Substitution Operators on Some Function Spaces

PMThe studies involving composition of functions have been pursued for a long time but the study of linear operators induced by composition with fixed functions has relatively a short story.In the begining composition operators were known as substitution operators. The adjoint of the unilateral shift operator on l^2(N) and bilateral shift operator on l^2(Z) are well studied examples of composition operators. The systematic study of composition (substitution) operators was started by Eric A. Nordgren in 1968. These operators have been the subject matter of study over the past 40 years.The applications of substitution operators are very much used in engineering and science