Geodesic
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

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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},
     publisher = {mathdoc},
     volume = {303},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2003_303_a13/}
}
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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/