The Bergman kernel on certain weakly pseudoconvex domains.

N. Watts Gebelt

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We compute the Bergman kernel functions of the unbounded domains $Ω_{p} = (z^{'}, z) \in ℂ ² : z > p (z^{'})$ , where $p (z^{'}) = {| z^{'} |}^{α} / α$ . It is also shown that these kernel functions have no zeros in $Ω_{p}$ . We use a method from harmonic analysis to reduce the computation of the 2-dimensional case to the problem of finding the kernel function of a weighted space of entire functions in one complex variable.

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