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Bergman Kernel in Complex Analysis

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Abstract

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.

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Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, Department of Mathematics, Jagiellonian University, Kraków, Poland

    Łukasz Kosiński & Włodzimierz Zwonek

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  1. Łukasz Kosiński
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  2. Włodzimierz Zwonek
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Correspondence to Włodzimierz Zwonek .

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  1. Earl Katz Chair in Algebraic System Theory, Department of Mathematics, Ben-Gurion University of the Negev, Be’er Sheva, Israel

    Daniel Alpay

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Kosiński, Ł., Zwonek, W. (2015). Bergman Kernel in Complex Analysis. In: Alpay, D. (eds) Operator Theory. Springer, Basel. https://doi.org/10.1007/978-3-0348-0667-1_68

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