From Semiclassical Strichartz Estimates to Uniform $L^p$ Resolvent Estimates on Compact Manifolds.

We prove uniform $$L^p$$ resolvent estimates for the stationary damped wave operator. The uniform $$L^p$$ resolvent estimates for the Laplace operator on a compact smooth Riemannian manifold without boundary were first established by Dos Santos Ferreira–Kenig–Salo [ 7 ] and advanced further by Bourgain–Shao–Sogge–Yao [ 2 ]. Here, we provide an alternative proof relying on the techniques of semiclassical Strichartz estimates. This approach allows us also to handle non-self-adjoint perturbations of the Laplacian and embeds very naturally in the semiclassical spectral analysis framework. [ABSTRACT FROM AUTHOR]