Geodesic
Zeros of bounded holomorphic functions in strictly pseudoconvex domains in ℂ 2
Annales de l'Institut Fourier, Tome 43 (1993) no. 2, pp. 437-458

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Let D be a bounded strictly pseudoconvex domain in ℂ 2 and let X be a positive divisor of D with finite area. We prove that there exists a bounded holomorphic function f such that X is the zero set of f. This result has previously been obtained by Berndtsson in the case where D is the unit ball in ℂ 2 .

Soit D un domaine strictement pseudoconvexe borné dans ℂ 2 , et soit X un diviseur positif de D d’aire finie. On montre l’existence d’une fonction bornée f dont X est l’ensemble des zéros de f. Ceci généralise un résultat de B. Berndtsson dans le cas où D est la boule unité de ℂ 2 .

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     author = {Arlebrink, Jim},
     title = {Zeros of bounded holomorphic functions in strictly pseudoconvex domains in ${\mathbb {C}}^2$},
     journal = {Annales de l'Institut Fourier},
     pages = {437--458},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {43},
     number = {2},
     year = {1993},
     doi = {10.5802/aif.1339},
     mrnumber = {94f:32021},
     zbl = {0782.32013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.5802/aif.1339/}
}
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Arlebrink, Jim. Zeros of bounded holomorphic functions in strictly pseudoconvex domains in ${\mathbb {C}}^2$. Annales de l'Institut Fourier, Tome 43 (1993) no. 2, pp. 437-458. doi: 10.5802/aif.1339

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