Adjoints of linear fractional composition operators on [formula omitted

Abstract

Given φ:D→D, an analytic self-map of the unit disc in C, the composition operator Cφ is defined by Cφ(f)=f∘φ for f belonging to some Hilbert space of analytic functions on D. We present a formula for the adjoint of linear-fractionally induced composition operators on S2(D), a weighted Hardy space, which consists of analytic functions on the disc whose first derivative is in H2(D).