The Bergman kernel function
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...
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The boundary behavior of the Bergman Kernel function of some Reinhardt domains is studied. Upper and lower bounds for the Bergman kernel function are found at the diagonal points (z, z̄). Let D be the Reinhardt domain D = { z ∈ C | ‖z‖α = n ∑
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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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Let (L, h) → (X,ω) be a compact toric polarized Kähler manifold of complex dimension n. For each k ∈ N, the fibre-wise Hermitian metric h on L induces a natural inner product on the vector space C∞(X,Lk) of smooth global sections of L by integration with respect to the volume form ω n n! . The orthogonal projection Pk : C∞(X,Lk) → H(X,L) onto the space H(X,L) of global holomorphic sections of L...
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ژورنال
عنوان ژورنال: Indian Journal of Pure and Applied Mathematics
سال: 2010
ISSN: 0019-5588,0975-7465
DOI: 10.1007/s13226-010-0010-4