Exitation of the wave field in the triangular domain with impedance boundary conditions

The equation of Helmholtz in a close domain which is an equilateral triangle with nonhomogeneous impedance boundary conditions is considered. The functional equation in which an unknown function is Fourier-image of the wave field on the boundary of the domain is constracted. This functional equation is solved for the case of the homogeneous boundary conditions (the problem on eigenvalues) as well as for the case of the nonhomogeneous boundary conditions in the absence of the resonance.