The Bergman kernel functions of certain unbounded domains

Friedrich Haslinger

Annales Polonici Mathematici (1998)

  • Volume: 70, Issue: 1, page 109-115
  • ISSN: 0066-2216

Abstract

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We compute the Bergman kernel functions of the unbounded domains Ω p = ( z ' , z ) ² : z > p ( z ' ) , where p ( z ' ) = | z ' | α / α . It is also shown that these kernel functions have no zeros in Ω p . We use a method from harmonic analysis to reduce the computation of the 2-dimensional case to the problem of finding the kernel function of a weighted space of entire functions in one complex variable.

How to cite

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Friedrich Haslinger. "The Bergman kernel functions of certain unbounded domains." Annales Polonici Mathematici 70.1 (1998): 109-115. <http://eudml.org/doc/262543>.

@article{FriedrichHaslinger1998,
abstract = {We compute the Bergman kernel functions of the unbounded domains $Ω_p = \{(z^\{\prime \},z) ∈ ℂ² : z > p(z^\{\prime \})\}$, where $p(z^\{\prime \}) = |z^\{\prime \}|^\{α\}/α$. It is also shown that these kernel functions have no zeros in $Ω_p$. We use a method from harmonic analysis to reduce the computation of the 2-dimensional case to the problem of finding the kernel function of a weighted space of entire functions in one complex variable.},
author = {Friedrich Haslinger},
journal = {Annales Polonici Mathematici},
keywords = {Bergman kernel; Szegő kernel; Bergman and Szegő kernel functions; entire functions; weakly pseudoconvex domains; integral representations in },
language = {eng},
number = {1},
pages = {109-115},
title = {The Bergman kernel functions of certain unbounded domains},
url = {http://eudml.org/doc/262543},
volume = {70},
year = {1998},
}

TY - JOUR
AU - Friedrich Haslinger
TI - The Bergman kernel functions of certain unbounded domains
JO - Annales Polonici Mathematici
PY - 1998
VL - 70
IS - 1
SP - 109
EP - 115
AB - We compute the Bergman kernel functions of the unbounded domains $Ω_p = {(z^{\prime },z) ∈ ℂ² : z > p(z^{\prime })}$, where $p(z^{\prime }) = |z^{\prime }|^{α}/α$. It is also shown that these kernel functions have no zeros in $Ω_p$. We use a method from harmonic analysis to reduce the computation of the 2-dimensional case to the problem of finding the kernel function of a weighted space of entire functions in one complex variable.
LA - eng
KW - Bergman kernel; Szegő kernel; Bergman and Szegő kernel functions; entire functions; weakly pseudoconvex domains; integral representations in
UR - http://eudml.org/doc/262543
ER -

References

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