Spectral Properties of the Massless Relativistic Harmonic Oscillator

Abstract

The spectral properties of the pseudo-differential operator $(-d^2/d{x}^2{)}^{1/2}+x^2$ are analyzed by a combination of functional integration methods and direct analysis. We obtain a representation of its eigenvalues and eigenfunctions, prove precise asymptotic formulae, and establish various analytic properties. We also derive trace asymptotics and heat kernel estimates.

21 pages, 0 figures

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