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arXiv · 1507.04850

The Bargmann transform and powers of harmonic oscillator on Gelfand-Shilov subspaces

Carmen Fernandez·Antonio Galbis·Joachim Toft
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Abstract

We consider the counter images $\maclJ (\rr d)$ and $\maclJ _0(\rr d)$ of entire functions with exponential and almost exponential bounds, respectively, under the Bargmann transform, and we characterize them by estimates of powers of the harmonic oscillator. We also consider the Pilipovi{\'c} spaces $\bsycalS _s(\rr d)$ and $\bsySig _s(\rr d)$ when $0<s<1/2$ and deduce their images under the Bargmann transform.

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Carmen Fernandez, Antonio Galbis, Joachim Toft. 2015-07-17. The Bargmann transform and powers of harmonic oscillator on Gelfand-Shilov subspaces. https://arxiv.org/abs/1507.04850

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