Breakdown of analyticity for d-bar-b and Szego kernels
Abstract
The CR manifold Mm = Im z2= Re z12m (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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