Breakdown of analyticity for d-bar-b and Szego kernels

Details Breakdown of analyticity for d-bar-b and Szego kernels Breakdown of analyticity for d-bar-b and Szego kernels

1996-07-29

arxiv.org/abs/math/9607201v1

Mathematics

Complex Variables

Scientific paper

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.

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