Title: Viscosity limits for 0th order operators
Abstract: In recent work, Colin de Verdiere--Saint-Raymond and Dyatlov--Zworski showed that a class of zeroth order pseudodifferential operators coming from experiments on forced waves in fluids satisfies a limiting absorption principle. Thus, these operators have absolutely continuous spectrum with possibly finitely many embedded eigenvalues. In this talk, we discuss the effect of small viscosity on the spectra of these operators, showing that the spectrum of the operator with small viscosity converges to the poles of a certain meromorphic continuation of the resolvent through the continuous spectrum. In order to do this, we introduce spaces based on an FBI transform which allows for the testing of microlocal analyticity properties. This talk is based on joint work with M. Zworski.
for zoom meeting information please contact dmitry.jakobson [at] mcgill.ca