Trapped Rays in Cylindrically Symmetric Media and Poles of the Analytically Continued Resolvent

The acoustic stratified. propagator is defined as the positive self-adjoint operator K ʹ yc2 y.r y.=zry1 y.=z on L 2 Rn, c2r.y1dnz., where zs x,y. xgRk, ygRm. Bounds on the weighted resolvent of K, defined as z:ya Kyz.y1 z:ya for a )1r2 and z:s 1q