Viscosity Limits for Zeroth‐Order Pseudodifferential Operators

Motivated by the work of Colin de Verdière and Saint-Raymond on spectral theory for zeroth-order pseudodifferential operators tori, we consider viscosity limits in which operators, P, are replaced P + iν Δ, ν > 0. By adapting Helffer–Sjöstrand scattering resonances, show that, a complex neighbourhood continuous spectrum, eigenvalues Δ have as goes to In simplified setting this justifies claims made physics literature. © 2021 The Authors. Communications Pure Applied Mathematics published Wiley Periodicals LLC.