Semiclassical Gevrey operators and magnetic translations

TL;DR

This paper investigates semiclassical Gevrey pseudodifferential operators on Bargmann space, demonstrating their boundedness on weighted holomorphic function spaces for Gevrey indices of two or higher, using time frequency analysis techniques.

Contribution

It introduces bounds for semiclassical Gevrey operators on Bargmann spaces, extending understanding of their behavior in weighted holomorphic function spaces.

Findings

Operators are uniformly bounded on weighted spaces for Gevrey index ≥ 2

Utilizes time frequency analysis methods in the context of pseudodifferential operators

Provides new insights into the behavior of semiclassical Gevrey operators

Abstract

We study semiclassical Gevrey pseudodifferential operators acting on the Bargmann space of entire functions with quadratic exponential weights. Using some ideas of the 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 $\geq 2$.