Zero-sets for $H^\infty$-functions on hyperplanes in $\mathbb B^n$
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 31, Tome 303 (2003), pp. 272-278
Cet article a éte moissonné depuis la source Math-Net.Ru
Let $\mathbb B^n$ be the unit ball in $\mathbb C^n$, $n\ge2$. We put $T_a=\{z\in\mathbb B^n:(z,a)=|a|^2\}$ for $a\in\mathbb B^n$ and $T_A=\bigcup\limits_{a\in A}T_a$ for a discrete in $\mathbb B^n$ set $A$. We find a sharp necessary condition for a set $A$ to be a part of the zero-set for a function in $H^\infty(\mathbb B^n)$.
@article{ZNSL_2003_303_a13,
author = {N. A. Shirokov},
title = {Zero-sets for $H^\infty$-functions on hyperplanes in~$\mathbb B^n$},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {272--278},
year = {2003},
volume = {303},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2003_303_a13/}
}
N. A. Shirokov. Zero-sets for $H^\infty$-functions on hyperplanes in $\mathbb B^n$. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 31, Tome 303 (2003), pp. 272-278. http://geodesic.mathdoc.fr/item/ZNSL_2003_303_a13/
[1] G. M. Khenkin, “Postroenie funktsii klassa Nevanlinny s predpisannymi nulyami v strogo psevdovypukloi oblasti”, DAN SSSR, 224:1 (1975), 10–13
[2] H. Skoda, “Valeurs au bord pour l'opérateur $d$ et zeros des fonctions de la class de Nevanlinna”, Bull. Soc. Math. France, 104 (1976), 225–299 | MR | Zbl
[3] N. A. Shirokov, “Sledy funktsii iz $H^\infty(\mathbb{B}^n)$ na nekotorom mnozhestve giperploskostei”, Zap. nauchn. semin. LOMI, 141, 1985, 183–187 | MR | Zbl
[4] A. B. Aleksandrov, “Uslovie Blyashke i korni ogranichennykh funktsii”, Mnogomernyi kompleksnyi analiz, Krasnoyarsk, 1985, 23–26 | MR