Integral Equations and Operator Theory

, Volume 11, Issue 2, pp 151–160

Linear fractional composition operators on H2

  • Carl C. Cowen
Article

DOI: 10.1007/BF01272115

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

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.

Copyright information

© Birkhäuser Verlag 1988

Authors and Affiliations

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