We study semiclassical Gevrey pseudodifferential operators acting on the Bargmann space of entire functions with quadratic exponential weights. Using some ideas from time frequency analysis, we show that such operators are uniformly bounded on a natural scale of exponentially weighted spaces of holomorphic functions, provided that the Gevrey index is greater than or equal to 2.
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Michael Hitrik, Richard Lascar, Johannes Sjöstrand, Maher Zerzeri, Semiclassical Gevrey operators and magnetic translations. J. Spectr. Theory 12 (2022), no. 1, pp. 53–82DOI 10.4171/JST/394