Integral Equations and Operator Theory

, Volume 11, Issue 2, pp 151–160 | Cite as

Linear fractional composition operators on H2

  • Carl C. Cowen
Article

Abstract

If ϕ is an analytic function mapping the unit diskD into itself, the composition operatorCϕ is the operator onH2 given byCϕf=foϕ. The structure of the composition operatorCϕ 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
$$\varphi \left( z \right) = \frac{{az + b}}{{cz + d}}$$
for some complex numbersa, b, c, d such that ϕ maps the unit diskD 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.

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Copyright information

© Birkhäuser Verlag 1988

Authors and Affiliations

  • Carl C. Cowen
    • 1
  1. 1.Department of MathematicsPurdue UniversityWest LafayetteUSA

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