Common hypercyclic functions for multiples of convolution and non-convolution operators

Bernal-González, Luis

doi:10.1090/S0002-9939-09-09943-2

Common hypercyclic functions for multiples of convolution and non-convolution operators
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by Luis Bernal-González

Proc. Amer. Math. Soc. 137 (2009), 3787-3795

DOI: https://doi.org/10.1090/S0002-9939-09-09943-2

Published electronically: June 5, 2009

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Abstract:

We prove the existence of a residual set of entire functions, all of whose members are hypercyclic for every non-zero scalar multiple of $T$, where $T$ is the differential operator associated to an entire function of order less than $1/2$. The same result holds if $T$ is a finite-order linear differential operator with non-constant coefficients.

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