Results 1 to 10 of about 233 (146)
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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Algebraicity of the Bergman kernel
Mathematische Annalen, 2023 Our main result introduces a new way to characterize two-dimensional finite ball quotients by algebraicity of their Bergman kernels. This characterization is particular to dimension two and fails in higher dimensions, as is illustrated by a counterexample in dimension three constructed in this paper.
Peter Ebenfelt, Ming Xiao, Hang Xu
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Weighted Bergman kernels and virtual Bergman kernels [PDF]
Science in China Series A: Mathematics, 2005 12 pages. One-hour lecture for graduate students, SCV 2004, August 2004, Beijing, P.R. China.
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Bergman Kernel from Path Integral [PDF]
Communications in Mathematical Physics, 2009 We rederive the expansion of the Bergman kernel on Kahler manifolds developed by Tian, Yau, Zelditch, Lu and Catlin, using path integral and perturbation theory, and generalize it to supersymmetric quantum mechanics. One physics interpretation of this result is as an expansion of the projector of wave functions on the lowest Landau level, in the ...
Douglas, Michael, Klevtsov, Semyon
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Bergman kernels of elementary Reinhardt domains [PDF]
Pacific Journal of Mathematics, 2020 Typos corrected.
Chakrabarti, Debraj +3 more
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Off-Spectral Analysis of Bergman Kernels [PDF]
Communications in Mathematical Physics, 2020 AbstractThe asymptotic analysis of Bergman kernels with respect to exponentially varying measures near emergent interfaces has attracted recent attention. Such interfaces typically occur when the associated limiting Bergman density function vanishes on a portion of the plane,the off-spectral region.
Hedenmalm, Haakan, Wennman, Aron
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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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