Bohr property of bases in the space of entire functions and its generalizations
| Autor: | Aytuna, Aydin, Djakov, Plamen |
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| Rok vydání: | 2012 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1112/blms/bds120 |
| Popis: | We prove that if $(\varphi_n)_{n=0}^\infty, \; \varphi_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 $f= \sum_{n=0}^\infty f_n \varphi_n$ we have $\sum_{n=0}^\infty |f_n|\, \sup_{K}|\varphi_n| \leq \sup_{K_1} |f|.$ A similar assertion holds for bases in the space of global analytic functions on a Stein manifold with the Liouville Property. Comment: This version is accepted for publication in the Bulletin of the London Mathematical Society |
| Databáze: | arXiv |
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