Singularities of the Bergman kernel for certain weakly pseudoconvex domains
| dc.creator | Kamimoto, Joe | |
| dc.date | 1996-06-26 | |
| dc.date.accessioned | 2026-07-07T09:15:33Z | |
| dc.date.available | 2026-07-07T09:15:33Z | |
| dc.description | Consider the Bergman kernel $K^B(z)$ of the domain $\ellip = \{z \in \Comp^n ; \sum_{j=1}^n |z_j|^{2m_j}<1 \}$, where $m=(m_1,\ldots,m_n) \in \Natl^n$ and $m_n \neq 1$. Let $z^0 \in \partial \ellip$ be any weakly pseudoconvex point, $k \in \Natl$ the degenerate rank of the Levi form at $z^0$. An explicit formula for $K^B(z)$ modulo analytic functions is given in terms of the polar coordinates $(t_1, \ldots, t_k, r)$ around $z^0$. This formula provides detailed information about the singularities of $K^B(z)$, which improves the result of A. Bonami and N. Lohoué \cite{bol}. A similar result is established also for the Szegö kernel $K^S(z)$ of $\ellip$. | |
| dc.identifier | https://arxiv.org/abs/math/9606202 | |
| dc.identifier | http://arxiv.org/abs/math/9606202 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/153052 | |
| dc.subject | Complex Variables | |
| dc.subject | 32 | |
| dc.title | Singularities of the Bergman kernel for certain weakly pseudoconvex domains | |
| dc.type | text |