In this paper, we generalize a result recently obtained by the author. We characterize the cyclic vectors in $\Lp$. Let $f\in\Lp$ and $f\poly$ be contained in the space. We show that $f$ is non-vanishing if and only if $f$ is cyclic.

Keywords:

weighted $L^p$ spaces of entire functions, cyclic vectors weighted $L^p$ spaces of entire functions, cyclic vectors

MSC Classifications:

47A16, 46J15, 46H25 show english descriptions Cyclic vectors, hypercyclic and chaotic operators
Banach algebras of differentiable or analytic functions, $H^p$-spaces [See also 30H10, 32A35, 32A37, 32A38, 42B30]
Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX) 47A16 - Cyclic vectors, hypercyclic and chaotic operators
46J15 - Banach algebras of differentiable or analytic functions, $H^p$-spaces [See also 30H10, 32A35, 32A37, 32A38, 42B30]
46H25 - Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)

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