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arXiv · 1306.6866

On the inverse to the harmonic oscillator

Marco Cappiello·Luigi Rodino·Joachim Toft
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Abstract

Let $b_d$ be the Weyl symbol of the inverse to the harmonic oscillator on $\R^d$. We prove that $b_d$ and its derivatives satisfy convenient bounds of Gevrey and Gelfand-Shilov type, and obtain explicit expressions for $b_d$. In the even-dimensional case we characterize $b_d$ in terms of elementary functions. In the analysis we use properties of radial symmetry and a combination of different techniques involving classical a priori estimates, commutator identities, power series and asymptotic expansions.

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Marco Cappiello, Luigi Rodino, Joachim Toft. 2013-06-28. On the inverse to the harmonic oscillator. https://arxiv.org/abs/1306.6866

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