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Functions Universal for all Translation Operators in Several Complex Variables

Published online by Cambridge University Press:  20 November 2018

Frédéric Bayart  and
Paul M Gauthier
Frédéric Bayart
Affiliation:
Université Clermont Auvergne, CNRS, LMBP, F-63000 Clermont-Ferrand, France. e-mail: frederic.bayart@uca.fr
Paul M Gauthier
Affiliation:
Département demathématiques et de statistique, Université deMontréal, CP-6128A Centreville, Montréal, QC, H3C3J7, Canada. e-mail: gauthier@dms.umontreal.ca
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Abstract

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We prove the existence of a (in fact many) holomorphic function $f$ in ${{\mathbb{C}}^{d}}$ such that, for any $a\ne 0$, its translations $f(\cdot +na)$ are dense in $H({{\mathbb{C}}^{d}})$.

Keywords

47A1632E20hypercyclic operatortranslation operator
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 60 , Issue 3 , 01 September 2017 , pp. 462 - 469
Copyright
Copyright © Canadian Mathematical Society 2017

References

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