**On square roots of self-adjoint weighted composition operators on H ^{2}**

In this talk, we characterize square roots of self-adjoint weighted composition operators on the Hardy space H^{2}, i.e., W_{g, ψ} such that W_{g, ψ} =W_{f, Φ}^{2} is self-adjoint. In particular, we find symbol functions f and Φ in this case. Some of W_{f, Φ} may be other, nonself-adjoint weighted composition operators. We also investigate several properties of such W_{f, Φ}. Finally, we give equivalent conditions for such W_{f, Φ} to be self-adjoint or normal, respectively.

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This research was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education, Science and Technology(2016R1D1A1B03931937).