, Volume 52, Issue 2, pp 431-456

On the spectrum of certain noncommutative harmonic oscillators

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Abstract

Some spectral properties of certain 2×2 globally elliptic systems of ordinary differential operators, a class of vector-valued deformations of the classical harmonic oscillator here called noncommutative harmonic oscillators, will be described, with special emphasis on the Poisson relation and clustering properties of the eigenvalues.

Keywords: Clustering theorems, Periodic trajectories, Poisson relations, Noncommutative harmonic oscillators