0000000001090747
AUTHOR
Maher Zerzeri
Semiclassical Gevrey operators and magnetic translations
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 $\geq 2$.
Semiclassical Gevrey operators on exponentially weighted spaces of holomorphic functions
We provide a general overview of the recent works [“Semiclassical Gevrey operators in the complex domain”, Ann. Inst. Fourier (to appear), arXiv:2009.09125 (opens in new tab); J. Spectr. Theory 12, No. 1, 53–82 (2022; Zbl 1486.30104)] by the authors, devoted to continuity properties of semiclassical Gevrey pseudodifferential operators acting on a natural scale of exponentially weighted spaces of entire holomorphic functions.
Resonances over a potential well in an island
In this paper we study the distribution of scattering resonances for a multidimensional semi-classical Schr\"odinger operator, associated to a potential well in an island at energies close to the maximal one that limits the separation of the well and the surrounding sea.