The Szeg\H{o} kernel in analytic regularity and analytic Fourier Integral Operators
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...
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Main Author | |
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Format | Journal Article |
Language | English |
Published |
27.06.2023
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Subjects | |
Online Access | Get full text |
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Summary: | 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. |
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DOI: | 10.48550/arxiv.2306.15382 |