arXiv subjects

Ophélie Rouby

Publications and source records attributed to Ophélie Rouby.

3 recordsLinked to original sources

arXiv2020

Analytic Bergman operators in the semiclassical limit

Transposing the Berezin quantization into the setting of analytic microlocal analysis, we construct approximate semiclassical Bergman projections on weighted $L^2$ spaces with analytic weights, and show that their kernel functions admit an asymptotic expansion in the class of analytic symbols. As a corollary, we obtain new estimates for asymptotic expansions of the Bergman kernel on $\mathbb{C}^n$ and for high powers of ample holomorphic line bundles over compact complex manifolds.

math.AP↗

arXiv2017

Berezin-toeplitz quantization and complex weyl quantization of the torus t${}^2$

In this paper, we give a correspondence between the Berezin-Toeplitz and the complex Weyl quantizations of the torus $ \mathbb{T}^2$. To achieve this, we use the correspondence between the Berezin-Toeplitz and the complex Weyl quantizations of the complex plane and a relation between the Berezin-Toeplitz quantization of a periodic symbol on the real phase space $\mathbb{R}^2$ and the Berezin-Toeplitz quantization of a symbol on the torus $ \mathbb{T}^2 $.

math-ph↗

arXiv2015

Bohr-Sommerfeld quantization conditions for non-selfadjoint perturbations of selfadjoint operators in dimension one

In this paper, we give a description of the spectrum of a class of non-selfadjoint perturbations of selfadjoint operators in dimension one and we show that it is given by Bohr-Sommerfeld quantization conditions. To achieve this, we make use of previous work by Michael Hitrik, Anders Melin and Johannes Sj{ö}strand. We also give an application of our result in the case of PT-symmetric pseudo-differential operators.

math.SP↗