Using coordinates (x,y)βRΓRdβ1, we introduce
the notion that an unbounded domain in Rd is star shaped with
respect to x=Β±β. For such domains, we prove estimates on the
resolvent of the Dirichlet Laplacian near the continuous spectrum. When the
domain has infinite cylindrical ends, this has consequences for wave decay and
resonance-free regions. Our results also cover examples beyond the star-shaped
case, including scattering by a strictly convex obstacle inside a straight
planar waveguide.Comment: 21 pages, 5 figure