The Bergman kernel functions of certain unbounded domains

Friedrich Haslinger

Annales Polonici Mathematici, Tome 69 (1998), p. 109-115 / Harvested from The Polish Digital Mathematics Library

Résumé

We compute the Bergman kernel functions of the unbounded domains $Ω_{p} = (z^{'}, z) \in ℂ ² : z > p (z^{'})$ , 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.

Publié le : 1998-01-01

Zbl 0929.32005

EUDML-ID : urn:eudml:doc:262543

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     author = {Friedrich Haslinger},
     title = {The Bergman kernel functions of certain unbounded domains},
     journal = {Annales Polonici Mathematici},
     volume = {69},
     year = {1998},
     pages = {109-115},
     zbl = {0929.32005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv70z1p109bwm}
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Friedrich Haslinger. The Bergman kernel functions of certain unbounded domains. Annales Polonici Mathematici, Tome 69 (1998) pp. 109-115. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv70z1p109bwm/

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