Bergman kernels of elementary Reinhardt domains
Copyright policy )Bergman kernels of elementary Reinhardt domains
We study the Bergman kernel of certain domains in $\mathbb{C}^n$, called elementary Reinhardt domains, generalizing the classical Hartogs triangle. For some elementary Reinhardt domains, we explicitly compute the kernel, which is a rational function of the coordinates. For some other such domains, we show that the kernel is not a rational function. For a general elementary Reinhardt domain, we obtain a representation of the kernel as an infinite series.
Typos corrected. To appear in Pacific Journal of Mathematics
- Central Michigan University United States
Mathematics - Complex Variables, Integral representations; canonical kernels (Szegő, Bergman, etc.), FOS: Mathematics, generalized Hartogs triangle, Special domains (Reinhardt, Hartogs, circular, tube, etc.) in \(\mathbb{C}^n\) and complex manifolds, Complex Variables (math.CV), Bergman kernel, 32A25, 32A07
Mathematics - Complex Variables, Integral representations; canonical kernels (Szegő, Bergman, etc.), FOS: Mathematics, generalized Hartogs triangle, Special domains (Reinhardt, Hartogs, circular, tube, etc.) in \(\mathbb{C}^n\) and complex manifolds, Complex Variables (math.CV), Bergman kernel, 32A25, 32A07
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