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Title: On the essential spectrum of certain non-commutative oscillators

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.
Authors:
;  [1]
  1. Department of Mathematics, University of Bologna, Piazza di Porta S.Donato 5, 40126 Bologna (Italy)
Publication Date:
OSTI Identifier:
22250909
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 54; Journal Issue: 12; Other Information: (c) 2013 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COMMUTATION RELATIONS; HARMONIC OSCILLATORS; SPECTRA