Limiting Amplitude principle in the scattering by wedges

We consider a nonstationary scattering of plane waves by a wedge. We prove that the Sommerfeld-type integral, constructed in (Math. Meth. Appl. Sci. 2005; 28:147-183; Proc. Int. Seminar "Day on Diffraction-2003", University of St. Petersburg, 2003; 151-162), is a classical smooth solution from a functional space, and prove the Limiting Amplitude principle.