Canad. Math. Bull. 51(2008), 378-385
Printed: Sep 2008
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.
weighted $L^p$ spaces of entire functions, cyclic vectors
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)