In this paper the problem on the eigenvalues of the Cauchy-Riemann operator with homogeneous boundary conditions is reduced to an integral equation.

To solve the mixed problem for a partial differential equation with involution and a symmetric potential there was found an explicit analytical representation by the Fourier method. The problem was considered under general boundary conditions with constant coefficients by a space variable. At the same we used the methods for avoiding the termwise differentiation of a functional series and applying the minimal conditions on initial data of the problem.