2019/12/20 by Galkowski, Jeffrey, Zworski, Maciej
#Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.1912.09840
Motivated by the work of Colin de Verdière and Saint-Raymond on spectral theory 0th order pseudodifferential operators on tori we consider viscosity limits in which 0th order operators P are replaced by P + i νΔ, ν> 0 . By adapting the Helffer--Sjöstrand theory of scattering resonances we show that in a complex neighbourhood of the continuous spectrum eigenvalues of P + i νΔ have limits as viscosity ν goes to 0. In the simplified setting of tori this justifies claims made in the physics literature.