Quantitative Spectral Stability for compact operators

Giovanni Siclari - Centro De Giorgi
Quantitative Spectral Stability for compact operators

Abstract
In this talk, we discuss a quantitative spectral stability result for operators with compact resolvent acting on Hilbert spaces. Under fairly general assumptions, we provide a characterization of the dominant term of the asymptotic expansion of the eigenvalues variation in this abstract setting. Many of the results about quantitative spectral stability available in the literature can be recovered by our analysis. We illustrate the result with several examples including an application to a free boundary eigenvalues problem.