Asymptotics of the Transfer Function of the Poincar$$\acute{\text{e}}$$–Steklov Operator for a Functionally Graded Elastic Layer

We consider the Poincaré–Steklov operator for a three-dimensional boundary-value problem for a functionally graded elastic layer, which maps normal stresses into normal displacements on a part of the boundary. A three-term asymptotic expansion of the transfer function of this operator is obtained for large values of the Fourier transform parameters.