Meromorphic Continuation of the Semiclassical Resolvent for Normally Hyperbolic Trapped Sets via Escape Function Methods

This paper establishes the meromorphic continuation of the semiclassical resolvent associated to pseudodifferential operators with normally hyperbolic trapped sets. By employing escape function constructions and anisotropic Sobolev spaces (Dyatlov-Zworski framework), we define H_{G}^{s} := e^{-G^{w}/h}H^{s} to recover a Fredholm setting. The poles of the continued resolvent are shown to characterize the quantum resonances of the system.