Abstract
A nonlocal boundary problem for the Helmholtz operator in a half-disk is considered. The peculiarity of this problem from others is that Fourier method could not be applied directly to it. Because the corresponding spectral problem for the ordinary differential equation has the system of eigenfunctions which does not form a basis. Based on these eigenfunctions a special system of functions that already forms a basis is constructed. This system is used for solving the nonlocal boundary problem. Existence and uniqueness of the classical solution of the problem are proved.
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