Asymptotics of Eigenfunctions of the Bouncing Ball Typeof the Operator in a Domain Boundedby Semirigid Walls

We consider the problem on the semiclassical spectrum of the operator with Bessel-type degeneration on the boundary of a two-dimensional domain (semirigid walls). It is well known that the asymptotic eigenfunctions associated with Lagrangian manifolds can be constructed using a modification of the Maslov canonical operator. We obtain asymptotic eigenfunctions associated with the simplest periodic trajectories of the corresponding Hamiltonian system with reflections on the domain boundary.