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arXiv · 0704.0997

Stable algebras of entire functions

Dan Coman·Evgeny A. Poletsky
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Abstract

Suppose that $h$ and $g$ belong to the algebra $\B$ generated by the rational functions and an entire function $f$ of finite order on ${\Bbb C}^n$ and that $h/g$ has algebraic polar variety. We show that either $h/g\in\B$ or $f=q_1e^p+q_2$, where $p$ is a polynomial and $q_1,q_2$ are rational functions. In the latter case, $h/g$ belongs to the algebra generated by the rational functions, $e^p$ and $e^{-p}$.

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Dan Coman, Evgeny A. Poletsky. 2007-04-09. Stable algebras of entire functions. https://arxiv.org/abs/0704.0997

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