Solution of a $\mathbb R$-Linear Conjugation Problem for a Parallel-Layered Medium in the Class of Piecewise Meromorphic Functions

The problem of $\mathbb R$-linear conjugation for parallel-layered $(n+1)$-phase media is solved in the class of piecewise meromorphic functions with given principal parts. The solution is written as a left-sided Fourier integral with a known original. In addition, some sufficient conditions under which the Fourier integral can be represented as an absolutely convergent series are obtained.