Poisson and Szegö kernel scaling asymptotics on Grauert tube boundaries (after Zelditch, Chang and Rabinowitz)

Fuente: arXiv
Saved in:
Bibliographic Details
Main Author: Paoletti, Roberto
Format: Preprint
Published: 2023
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866929232223928320
author Paoletti, Roberto
author_facet Paoletti, Roberto
contents We review and elaborate on recent work of Chang and Rabinowitz on scaling asymptotics of Poisson and Szegö kernels on Grauert tubes, providing additional results that may be useful in applications. In particular, focusing on the near-diagonal case, we give an explicit description of the leading order terms, and an estimate on the growth of the degree of certain polynomials describing the rescaled asymptotics. Furthermore, we allow rescaled asymptotics in a range $O\left(λ^{ε-1/2}\right)$ in all the variables involved, where $λ\rightarrow+\infty$ is the asymptotic parameter, rather than rescale according to Heisenberg type.
format Preprint
id arxiv_https___arxiv_org_abs_2308_09317
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Poisson and Szegö kernel scaling asymptotics on Grauert tube boundaries (after Zelditch, Chang and Rabinowitz)
Paoletti, Roberto
Symplectic Geometry
Complex Variables
We review and elaborate on recent work of Chang and Rabinowitz on scaling asymptotics of Poisson and Szegö kernels on Grauert tubes, providing additional results that may be useful in applications. In particular, focusing on the near-diagonal case, we give an explicit description of the leading order terms, and an estimate on the growth of the degree of certain polynomials describing the rescaled asymptotics. Furthermore, we allow rescaled asymptotics in a range $O\left(λ^{ε-1/2}\right)$ in all the variables involved, where $λ\rightarrow+\infty$ is the asymptotic parameter, rather than rescale according to Heisenberg type.
title Poisson and Szegö kernel scaling asymptotics on Grauert tube boundaries (after Zelditch, Chang and Rabinowitz)
topic Symplectic Geometry
Complex Variables
url https://arxiv.org/abs/2308.09317