Addendum to “On the Bergman kernel of hyperconvex domains”, Nagoya Math. J. 129 (1993), 43–52

0. In [0-1] it was proved that for any bounded hyperconvex domain D in C2 the Bergman kernel function K(z, w) of D satisfiesIn case n ═ 1, this is due to a behavior of sublevel sets of the Green function. The general case then follows by the extendability of L2 holomorphic functions.

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On boundary behaviour of Bergman kernel function for plane domains and their Cartesian products

Banach Center Publications ◽

10.4064/-11-1-217-222 ◽

1983 ◽

Vol 11 (1) ◽

pp. 217-222

Author(s):

Ewa Ligocka

Keyword(s):

Kernel Function ◽

Bergman Kernel ◽

Boundary Behaviour ◽

Cartesian Products ◽

Bergman Kernel Function

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The Bergman kernel and the green function

Journal of Mathematical Sciences ◽

10.1007/bf02355588 ◽

1997 ◽

Vol 87 (2) ◽

pp. 3366-3380

Author(s):

V. A. Malyshev

Keyword(s):

Green Function ◽

Bergman Kernel ◽

The Green Function

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The Bergman kernel function: Explicit formulas and zeroes

Proceedings of the American Mathematical Society ◽

10.1090/s0002-9939-99-04570-0 ◽

1999 ◽

Vol 127 (3) ◽

pp. 805-811 ◽

Cited By ~ 30

Author(s):

Harold P. Boas ◽

Siqi Fu ◽

Emil J. Straube

Keyword(s):

Kernel Function ◽

Bergman Kernel ◽

Explicit Formulas ◽

Bergman Kernel Function

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The Bergman kernel function

Indian Journal of Pure and Applied Mathematics ◽

10.1007/s13226-010-0010-4 ◽

2010 ◽

Vol 41 (1) ◽

pp. 189-197 ◽

Cited By ~ 1

Author(s):

Gadadhar Misra

Keyword(s):

Kernel Function ◽

Bergman Kernel ◽

Bergman Kernel Function

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Some recent developments in the theory of the Bergman kernel function: a survey

Proceedings of Symposia in Pure Mathematics - Several Complex Variables ◽

10.1090/pspum/030.1/0442295 ◽

1977 ◽

pp. 127-137 ◽

Cited By ~ 4

Author(s):

Klas Diederich

Keyword(s):

Kernel Function ◽

Bergman Kernel ◽

Bergman Kernel Function ◽

Recent Developments

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An explicit computation of the Bergman kernel function

Journal of Geometric Analysis ◽

10.1007/bf02921591 ◽

1994 ◽

Vol 4 (1) ◽

pp. 23-34 ◽

Cited By ~ 25

Author(s):

John P. D’Angelo

Keyword(s):

Kernel Function ◽

Bergman Kernel ◽

Explicit Computation ◽

Bergman Kernel Function

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On the invariant differential metrics near pseudoconvex boundary points where the Levi form has corank one

Nagoya Mathematical Journal ◽

10.1017/s0027763000004414 ◽

1993 ◽

Vol 130 ◽

pp. 25-54 ◽

Cited By ~ 8

Author(s):

Gregor Herbort

Keyword(s):

Asymptotic Formula ◽

Bergman Kernel ◽

Closed Subspace ◽

Integral Kernel ◽

Holomorphic Functions ◽

Levi Form ◽

Explicit Computation ◽

Bergman Kernel Function ◽

General Domain ◽

Invariant Differential

Let D be a bounded domain in Cn; in the space L2(D) of functions on D which are square-integrable with respect to the Lebesgue measure d2nz the holomorphic functions form a closed subspace H2(D). Therefore there exists a well-defined orthogonal projection PD: L2(D) → H2(D) with an integral kernel KD:D × D → C, the Bergman kernel function of D. An explicit computation of this function directly from the definition is possible only in very few cases, as for instance the unit ball, the complex “ellipsoids” , or the annulus in the plane. Also, there is no hope of getting information about the function KD in the interior of a general domain. Therefore the question for an asymptotic formula for the Bergman kernel near the boundary of D arises.

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