The Bergman kernel function: Explicit formulas and zeroes
نویسندگان
چکیده
منابع مشابه
The Bergman Kernel Function
In this note, we point out that a large family of n × n matrix valued kernel functions defined on the unit disc D ⊆ C, which were constructed recently in [9], behave like the familiar Bergman kernel function on D in several different ways. We show that a number of questions involving the multiplication operator on the corresponding Hilbert space of holomorphic functions on D can be answered usi...
متن کاملZeroes of the Bergman kernel of Hartogs domains
We exhibit a class of bounded, strongly convex Hartogs domains with realanalytic boundary which are not Lu Qi-Keng, i.e. whose Bergman kernel function has a zero.
متن کاملExplicit formulas for the Green’s function and the Bergman kernel for monogenic functions in annular shaped domains in R
By applying a reflection principle we set up fully explicit representation formulas for the harmonic Green’s function for orthogonal sectors of the annulus of the unit ball of R. From the harmonic Green’s function we then can determine the Bergman kernel function of Clifford holomorphic functions by applying an appropriate vector differentiation. As a concrete application we give an explicit an...
متن کاملBergman Kernel, Deformation Quantization and Feynman Diagram Formulas
This expository article is an expanded version of the talk given by the author at the 2013 ICCM conference in Taipei. We report our recent work on explicit closed formulas of the asymptotic expansions of the Bergman kernel, and the relationship to deformation quantization on Kähler manifolds. These formulas are expressed as summations over strongly connected graphs.
متن کاملThe Bergman Kernel Function and Proper Holomorphic Mappings
It is proved that a proper holomorphic mapping / between bounded complete Reinhardt domains extends holomorphically past the boundary and that if, in addition, /~'(0) = {0}, then / is a polynomial mapping. The proof is accomplished via a transformation rule for the Bergman kernel function under proper holomorphic mappings.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1999
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-99-04570-0