| Abstract: | In the case of the scattering problem on a wedge and on a screen, for a certain class of boundary conditions, one constructs explicitly the wave operators and one establishes their completeness. It is shown that a modified scattering matrix (including additionally the reflection operator) is a unitary operator with a pure point spectrum. In the case of a screen, the standard S-matrix is unitary. For Dirichlet (Neumann) boundary conditions, the S-matrix is reduced explicitly to a diagonal form. The spectrum of the S-matrix is simple, absolutely continuous, filling the lower (upper) semicircumference.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 107, pp. 193–197, 1982. |
