On the essential spectrum of certain non-commutative oscillators
On the essential spectrum of certain non-commutative oscillators
We show here that the spectrum of the family of non-commutative harmonic oscillators \documentclass[12pt]{minimal}\begin{document}$Q_{(\alpha ,\beta )}^\mathrm{w}(x,D)$\end{document}Q(α,β)w(x,D) for \documentclass[12pt]{minimal}\begin{document}$\alpha ,\beta \in \mathbb {R}_+$\end{document}α,β∈R+ in the range αβ = 1 is [0, +∞) and is entirely essential spectrum. The previous existing results concern the case αβ > 1 (case in which \documentclass[12pt]{minimal}\begin{document}$Q_{(\alpha …