Mixing convolution operators on spaces of entire functions

2015/08/12 by V. V. Fávaro, Fávaro, V. V., J. Mujica +1
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #math.FA

paper · pdf · doi:10.48550/arxiv.1508.03066

17 pages

arxiv created 2015/08/12 · arxiv updated 2015/08/14

Abstract

We show that if E is an arbitrary (DFN)-space, then every nontrivial convolution operator on the Fréchet nuclear space H(E) is mixing, in particular hypercyclic. More generally we obtain the same conclusion when E=F^′_c, where F is a separable Fréchet space with the approximation property. On the opposite direction we show that a translation operator on the space H(ℂ^ℕ) is never hypercyclic.

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