| In this dissertation we systematically summarize the studies conducted in [2] and [9] about the possible region Rg⊂C on which we have uniform Lp → Lq estimates for resolvent operators (Delta g + zeta)--1, zeta ∈ Rg on a compact Riemannian manifold (M, g) with dimension n ≥ 2. These studies answer a question regarding the largest possible region Rg on a general compact manifold, raised by Kenig, Dos Santos Ferreira and Salo in [3], and extend this result on the torus Tn and compact manifolds with non-positive curvature, using the half-wave operator eit-Dg and techniques from the wave equation. |
