, Volume 279, Issue 2, pp 285-308
Date: 20 Feb 2008

On the Spectrum of Certain Non-Commutative Harmonic Oscillators and Semiclassical Analysis

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A localization and “cardinality” property, along with a multiplicity result, of the spectrum of certain 2 × 2 globally elliptic systems of ordinary differential operators, a class of vector-valued deformations of the classical harmonic oscillator called non-commutative harmonic oscillators, will be described here. The basic tool is the study of a semiclassical reference system.

Dedicated to Professor Cesare Parenti, friend and teacher, on the occasion of his sixty-fifth birthday.
Communicated by P. Sarnak