On the Essential Spectrum of Certain Non–Commutative Oscillators
نویسندگان
چکیده
We show here that the spectrum of the family of noncommutative harmonic oscillators Qw(α,β)(x,D) for 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 Qw(α,β)(x,D) is globally elliptic with a discrete spectrum whose qualitative properties are being extensively studied), and ours therefore extends the picture to the range of parameters αβ ≥ 1.
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