Friedrich Haslinger
The Bergman kernel functions for certain unbounded domains in
C2
(7 pages)
Abstract.
In this paper we compute the Bergman kernel functions of the
unbounded domains in C2
{(z1,z2) : Im z2 > p(z1) },
where p(z1) = |z1|a/a , a > 2.
It is also shown that these kernel functions have no zeroes in the above
domain. 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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