Department of Mathematics, Faculty of Science of Tunis, University of Tunis El-Manar, 1060, Tunis, Tunisia. E-mail: Sameh.Gana@fst.rnu.tn
AMS Subject Classification: 34L05, 34L40, 81Q20, 74S25.
In this paper, we first generalize the curves constructed by L.S. Boulton where he proves that the resolvent norm of the one-dimensional complex harmonic oscillator tends to infinity. Second, we give numerical computations of pseudo-spectra of the two-dimensional complex harmonic oscillator which permits to precise the spectral instability.
Complex harmonic oscillator, linear operators, pseudo-spectrum, semi-classical analysis, pseudo-differential operators, microlocal analysis
