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arXiv · 1201.5607

Bohr property of bases in the space of entire functions and its generalizations

Aydin Aytuna·Plamen Djakov
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Abstract

We prove that if $(φ_n)_{n=0}^\infty, \; φ_0 \equiv 1, $ is a basis in the space of entire functions of $d$ complex variables, $d\geq 1,$ then for every compact $K\subset \mathbb{C}^d$ there is a compact $K_1 \supset K$ such that for every entire function $f= \sum_{n=0}^\infty f_n φ_n$ we have $\sum_{n=0}^\infty |f_n|\, \sup_{K}|φ_n| \leq \sup_{K_1} |f|.$ A similar assertion holds for bases in the space of global analytic functions on a Stein manifold with the Liouville Property.

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Aydin Aytuna, Plamen Djakov. 2012-10-13. Bohr property of bases in the space of entire functions and its generalizations. https://doi.org/10.1112/blms%2Fbds120

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