Bergman kernel in complex analysis. (English) Zbl 1330.32002
Alpay, Daniel (ed.), Operator theory. With 51 figures and 2 tables. In 2 volumes. Basel: Springer (ISBN 978-3-0348-0666-4/print; 978-3-0348-0667-1/ebook; 978-3-0348-0668-8/print+ebook; 978-3-0348-0692-3/online (updated continuously)). Springer Reference, 73-86 (2015).
Summary: In this survey a brief review of results on the Bergman kernel and Bergman distance concentrating on those fields of complex analysis which remain in the focus of the research interest of the authors is presented. The topics discussed contain general discussion of \(\mathcal{L}_{\mathrm{h}}^{2}\) spaces, behavior of the Bergman distance, regularity of extension of proper holomorphic mappings, and recent development in the theory of Bergman distance stemming from the pluripotential theory and very short discussion of the Lu Qi Keng problem.
For the entire collection see [Zbl 1325.47001].
For the entire collection see [Zbl 1325.47001].
MSC:
| 32-02 | Research exposition (monographs, survey articles) pertaining to several complex variables and analytic spaces |
| 32A25 | Integral representations; canonical kernels (Szegő, Bergman, etc.) |
| 32A36 | Bergman spaces of functions in several complex variables |
| 32U05 | Plurisubharmonic functions and generalizations |
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