# Linear fractional composition operators on H^{2}

Article

- Received:

DOI: 10.1007/BF01272115

- Cite this article as:
- Cowen, C.C. Integr equ oper theory (1988) 11: 151. doi:10.1007/BF01272115

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## Abstract

If ϕ is an analytic function mapping the unit diskfor some complex numbers

*D*into itself, the composition operator*C*_{ϕ}is the operator on*H*^{2}given by*C*_{ϕ}f=foϕ. The structure of the composition operator*C*_{ϕ}is usually complex, even if the function ϕ is fairly simple. In this paper, we consider composition operators whose symbol ϕ is a linear fractional transformation mapping the disk into itself. That is, we will assume throughout that$$\varphi \left( z \right) = \frac{{az + b}}{{cz + d}}$$

*a, b, c, d*such that ϕ maps the unit disk*D*into itself. For this restricted class of examples, we address some of the basic questions of interest to operator theorists, including the computation of the adjoint.## Copyright information

© Birkhäuser Verlag 1988