The Szeg\H{o} kernel in analytic regularity and analytic Fourier Integral Operators
Spectral Theory
2023-06-28 v1 Functional Analysis
Abstract
We build a general theory of microlocal (homogeneous) Fourier Integral Operators in real-analytic regularity, following the general construction in the smooth case by H\"ormander and Duistermaat. In particular, we prove that the Boutet-Sj\"ostrand parametrix for the Szeg\H{o} projector at the boundary of a strongly pseudo-convex real-analytic domain can be realised by an analytic Fourier Integral Operator. We then study some applications, such as FBI-type transforms on compact, real-analytic Riemannian manifolds and propagators of one-homogeneous (pseudo)differential operators.
Keywords
Cite
@article{arxiv.2306.15382,
title = {The Szeg\H{o} kernel in analytic regularity and analytic Fourier Integral Operators},
author = {Alix Deleporte},
journal= {arXiv preprint arXiv:2306.15382},
year = {2023}
}