On the Cauchy problem for matrix factorizations of the Helmholtz equation in a bounded domain

In the paper it is considered the problem of regularization of the Cauchy problem for systems of elliptic type equations of the first order with constant coefficients factorisable Helmholtz operator in three-dimensional bounded domain. Using the results of [1–6], is constructed explicitly Carleman matrix and, based on the regularized solution of the Cauchy problem.