Breakdown of analyticity for d-bar-b and Szego kernels
Complex Variables
2009-09-25 v1
Abstract
The CR manifold M_m = { Im z_2= Re z_1^{2m} } (m=2,3,...) is the counterexample, which has been given by M. Christ and D. Geller, to analytic hypoellipticity of d-bar-b and real analyticity of the Szego kernel. In order to give a direct interpretation for the breakdown of real analyticity of the Szego kernel, we give a Borel summation type representation of the Szego kernel in terms of simple singular solutions of the equation d-bar-b u = 0.
Keywords
Cite
@article{arxiv.math/9607201,
title = {Breakdown of analyticity for d-bar-b and Szego kernels},
author = {Joe Kamimoto},
journal= {arXiv preprint arXiv:math/9607201},
year = {2009}
}