What Do Composition Operators Know About Inner Functions?
This paper gives several different ways in which operator norms characterize those composition operators \(\) that arise from holomorphic self-maps ϕ of the unit disc that are inner functions. The setting is the Hardy space H2 of the disc, and the key result is a characterization of inner functions in terms of the asymptotic behavior of the Nevanlinna counting function. The case \(\) offers an interesting surprise.
Unable to display preview. Download preview PDF.