Volume 9 (2026)
Deleporte, Alix
The Szegő kernel in analytic regularity and analytic Fourier integral operators
Annales Henri Lebesgue, Volume 9 (2026), pp. 607-675

Metadata

DOI10.5802/ahl.272
Keywords Szegő kernel ,  Toeplitz operators ,  analytic microlocal 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 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.


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