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Functions Universal for All Translation Operators in Several Complex Variables

  Published:2017-05-26
 Printed: Sep 2017
  • Frédéric Bayart,
    Clermont Université, Université Blaise Pascal, Laboratoire de Mathématiques, UMR 6620 - CNRS, Campus Universitaire des Cézeaux, 3, place Vasarely, TSA 60026, CS 60026, F-63 178 Aubière Cedex
  • Paul M Gauthier,
    Département de mathématiques et de statistique, Université de Montréal, CP-6128A Centreville, Montréal, QC, H3C3J7, Canada
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Abstract

We prove the existence of a (in fact many) holomorphic function $f$ in $\mathbb{C}^d$ such that, for any $a\neq 0$, its translations $f(\cdot+na)$ are dense in $H(\mathbb{C}^d)$.
Keywords: hypercyclic operator, translation operator hypercyclic operator, translation operator
MSC Classifications: 47A16, 32E20 show english descriptions Cyclic vectors, hypercyclic and chaotic operators
Polynomial convexity
47A16 - Cyclic vectors, hypercyclic and chaotic operators
32E20 - Polynomial convexity
 

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