Complex symmetric composition operators on weighted Hardy spaces.

Let φ be an analytic self-map of the open unit disk D. We study the complex symmetry of composition operators C_φ on weighted Hardy spaces induced by a bounded sequence. For any analytic self-map of D that is not an elliptic automorphism, we establish that if C_φ is complex symmetric, then either φ (0) = 0 or φ is linear. In the case of weighted Bergman spaces A²_α, we find the non-automorphic linear fractional symbols φ such that C_φ is complex symmetric. [ABSTRACT FROM AUTHOR]