The Szegő kernel in analytic regularity and analytic Fourier integral operators
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 Hörmander and Duistermaat. In particular, we prove that the Boutet–Sjöstrand parametrix for the Szegő 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.
Fields of Study & Subjects
Mathematical Analysis and Transform Methods
Numerical methods in inverse problems
Spectral Theory in Mathematical Physics
Publication details
- Journal / source
- Annales Henri Lebesgue
- Volume
- 9
- Pages
- 607–675
- Publication date
- 12 June 2026
- Language
- EN