Spectral asymptotics for nonselfadjoint harmonic oscillators

Victor Arnaiz (1) , Gabriel Rivière (2)

1 ICMAT - Instituto de Ciencias Matematicas
2 LMJL - Laboratoire de Mathématiques Jean Leray

We consider nonselfadjoint perturbations of semiclassical harmonic oscillators. Under appropriate dynamical assumptions, we establish some spectral estimates such as upper bounds on the resolvent near the real axis when no geometric control condition is satisfied.

Mots clés: Semiclassical analysis; Harmonic oscillators; Resolvent estimates; nonselfadjoint operators

Domaines: Physique mathématique [math-ph]; Théorie spectrale [math.SP]; Equations aux dérivées partielles [math.AP]

Victor Arnaiz, Gabriel Rivière. Spectral asymptotics for nonselfadjoint harmonic oscillators. 2018. ⟨hal-01942234v1⟩