Approximate solution of a Cauchy problem for the Helmholtz equation

A problem of reconstruction of the radiation field in a domain from experimental data given on a part of boundary is considered. For the model problem described by a Cauchy problem for the Helmholtz equation, an approximate method based on regularization in the frequency space is analysed. Convergence and stability are proved under a suitable choice of regularization parameter. Numerical implementation of the method is discussed.