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

References

Publications referenced by this paper.
Showing 1-10 of 26 references

Hypocoercive diffusion operators

  • C. Villani
  • International Congress of Mathematicians
  • 2006
1 Excerpt

Hypoelliptic estimates and spectral theory for Fokker-Planck Operators and Witten Laplacians

  • B. Helffer, F. Nier
  • Lect. Notes in Math. 1862,
  • 2005
2 Excerpts

A general result about pseudospectrum for Schrödinger operators

  • K. Pravda-Starov
  • Proc. R. Soc. Lond. A
  • 2004

Nier . Isotropic hypoellipticity and trend to the equilibrium for the FokkerPlanck equation with high degree potential

  • C. Stolk F. Hérau, J. Sjöstrand.
  • Arch . Ration . Mech . Anal .
  • 2004

Similar Papers

Loading similar papers…