Inverse boundary value problems in the Cauchy statement for harmonic functions

We study the inverse boundary value problem (problem (A)) in the Cauchy statement for an analytic function with unknown curve $\Gamma$. We solve the considered problem by two different methods. We obtain necessary and sufficient conditions for $\Gamma$ to be the unit circumference. With the help of the described methods we solve a modified Hadamard example. We give a generalization for the case of a doubly connected domain.