Semiclassical Gevrey operators and magnetic translations

Michael Hitrik; Richard Lascar; Johannes Sjöstrand; Maher Zerzeri

doi:10.4171/jst/394

JournalsjstVol. 12, No. 1pp. 53–82

Semiclassical Gevrey operators and magnetic translations

Michael Hitrik
University of California at Los Angeles, USA
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Richard Lascar
Université Côte d’Azur, Nice, France
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Johannes Sjöstrand
Université de Bourgogne 9, Dijon, France
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Maher Zerzeri
Université Sorbonne Paris-Nord, Villetaneuse, France
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Abstract

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.

Cite this article

Michael Hitrik, Richard Lascar, Johannes Sjöstrand, Maher Zerzeri, Semiclassical Gevrey operators and magnetic translations. J. Spectr. Theory 12 (2022), no. 1, pp. 53–82

DOI 10.4171/JST/394