2013/11/29 by Santiago Muro, Muro, Santiago, Damián Pinasco +3
Mathematics · #30D15 #47A16 #47B38 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:30D15 #msc:47A16 #msc:47B38
paper · pdf · doi:10.48550/arxiv.1311.7671
16 pages
arxiv created 2014/07/30 · arxiv updated 2014/07/31
A theorem of Godefroy and Shapiro states that non-trivial convolution operators on the space of entire functions on ℂn are hypercyclic. Moreover, it was shown by Bonilla and Grosse-Erdmann that they have frequently hypercyclic functions of exponential growth. On the other hand, in the infinite dimensional setting, the Godefroy-Shapiro theorem has been extended to several spaces of entire functions defined on Banach spaces. We prove that on all these spaces, non-trivial convolution operators are strongly mixing with respect to a gaussian probability measure of full support. For the proof we combine the results previously mentioned and we use techniques recently developed by Bayart and Matheron. We also obtain the existence of frequently hypercyclic entire functions of exponential growth.