Spectral Asymptotics for Large Skew-Symmetric Perturbations of the Harmonic Oscillator

@inproceedings{Gallagher2008SpectralAF,
title={Spectral Asymptotics for Large Skew-Symmetric Perturbations of the Harmonic Oscillator},
author={Isabelle Gallagher},
year={2008}
}

Originally motivated by a stability problem in Fluid Mechanics, we study the spectral and pseudospectral properties of the differential operator Hǫ = −∂2 x + x + iǫf(x) on L(R), where f is a real-valued function and ǫ > 0 a small parameter. We define Σ(ǫ) as the infimum of the real part of the spectrum of Hǫ, and Ψ(ǫ) −1 as the supremum of the norm of the resolvent of Hǫ along the imaginary axis. Under appropriate conditions on f , we show that both quantities Σ(ǫ), Ψ(ǫ) go to infinity as ǫ→ 0… CONTINUE READING