On the Cauchy problem for matrix factorizations of the Helmholtz equation in an unbounded domain in ${\mathbb R}^{2}$

In the paper it is considered the problem of regularization of the Cauchy problem for matrix factorisations of the Helmholtz equation in an unbounded planar domain. Using the Carleman matrix found an explicitly regularized solution of the Cauchy problem for matrix factorizations of the Helmholtz equation in two-dimensional unbounded domain.