2-Complex Symmetric Composition Operators on H2

In this paper, we study 2-complex symmetric composition operators with the conjugation J, defined by Jf(z)=<((f(z over bar )))over bar> over bar , on the Hardy space H-2. More precisely, we obtain the ($) over bar necessary and sufficient condition for the composition operator C-phi to be 2-complex symmetric with J when phi is an automorphism of D. We also characterize 2-complex symmetric with J when phi is a linear fractional self-map of D.

Automated summary

In this paper, we study the properties of 2-complex symmetric composition operators with the conjugation J in the Hardy space H-2, and provide the necessary and sufficient conditions for the composition operator to be 2-complex symmetric with J when the corresponding map is an automorphism or linear fractional self-map of D.