On the essential spectrum of certain non-commutative oscillators
Journal Article
·
· Journal of Mathematical Physics
- Department of Mathematics, University of Bologna, Piazza di Porta S.Donato 5, 40126 Bologna (Italy)
We show here that the spectrum of the family of non-commutative harmonic oscillators Q{sub (α,β)}{sup w}(x,D) for α,β∈R{sub +} in the range αβ = 1 is [0, +∞) and is entirely essential spectrum. The previous existing results concern the case αβ > 1 (case in which Q{sub (α,β)}{sup w}(x,D) is globally elliptic with a discrete spectrum whose qualitative properties are being extensively studied), and ours therefore extend the picture to the range of parameters αβ ⩾ 1.
- OSTI ID:
- 22250909
- Journal Information:
- Journal of Mathematical Physics, Vol. 54, Issue 12; Other Information: (c) 2013 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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