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Weighted Bergman kernels and virtual Bergman kernels [PDF]
Science in China Series A: Mathematics, 2004 We introduce the notion of "virtual Bergman kernel" and apply it to the computation of the Bergman kernel of "domains inflated by Hermitian balls", in particular when the base domain is a bounded symmetric domain.Comment: 12 pages.
A. Korányi +16 more
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Bergman kernels and symplectic reduction [PDF]
Comptes Rendus. Mathématique, 2005 We generalize several recent results concerning the asymptotic expansions of Bergman kernels to the framework of geometric quantization and establish an asymptotic symplectic identification property.
Ma, Xiaonan, Zhang, Weiping
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Optimal $L^2$ Extensions of Openness Type and Related Topics
Comptes Rendus. Mathématique, 2023 We establish several optimal $L^2$ extension theorems of openness type on weakly pseudoconvex Kähler manifolds. We prove a product property for certain minimal $L^2$ extensions, which generalizes the product property of Bergman kernels.
Xu, Wang, Zhou, Xiangyu
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On Weights Which Admit Harmonic Bergman Kernel and Minimal Solutions of Laplace’s Equation
Annales Mathematicae Silesianae, 2022 In this paper we consider spaces of weight square-integrable and harmonic functions L2H(Ω, µ). Weights µ for which there exists reproducing kernel of L2H(Ω, µ) are named ’admissible weights’ and such kernels are named ’harmonic Bergman kernels’. We prove
Żynda Tomasz Łukasz
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Reproducing Kernels for Hardy and Bergman Spaces of the Upper Half Plane
Communications in Advanced Mathematical Sciences, 2020 Using invertible isometries between Hardy and Bergman spaces of the unit disk $\D$ and the corresponding spaces of the upper half plane $\uP$, we determine explicitly the reproducing kernels for the Hardy and Bergman spaces of $\uP$. As a consequence, we
Job Bonyo
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Weighted Bergman Kernels and Mathematical Physics
Axioms, 2020 We review several results in the theory of weighted Bergman kernels. Weighted Bergman kernels generalize ordinary Bergman kernels of domains Ω ⊂ C n but also appear locally in the attempt to quantize classical states of mechanical systems ...
Elisabetta Barletta +2 more
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Superconnection and family Bergman kernels [PDF]
, 2006 We establish an asymptotic expansion for families of Bergman kernels. The key idea is to use the superconnection as in the local family index theorem.Comment: C. R. Math. Acad.
Ma, Xiaonan, Zhang, Weiping
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A remark on the approximation of plurisubharmonic functions [PDF]
, 2014 We show by an example that the Demailly approximation sequence of a plurisubharmonic function, constructed via Bergman kernels, is not a decreasing sequence in general.Comment: 4 pages, to appear in C. R. Math. Acad.
Kim, Dano
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On weights which admit the reproducing kernel of Bergman type
International Journal of Mathematics and Mathematical Sciences, 1992 In this paper we consider (1) the weights of integration for which the reproducing kernel of the Bergman type can be defined, i.e., the admissible weights, and (2) the kernels defined by such weights.
Zbigniew Pasternak-Winiarski
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Estimates on the Bergman Kernels in a Tangential Direction on Pseudoconvex Domains in C3
Abstract and Applied Analysis, 2018 Let Ω be a smoothly bounded pseudoconvex domain in C3 and assume that TΩreg(z0)
Sanghyun Cho
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