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Cyclic Vectors in Some Weighted Lp Spaces of Entire Functions

Published online by Cambridge University Press:  20 November 2018

Kou Hei Izuchi
Kou Hei Izuchi*
Affiliation:
Department of Mathematics, Graduate School of Science, Hokkaido University, Sapporo, Japan 060-0810. e-mail: khizuchi@math.sci.hokudai.ac.jp
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Abstract

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In this paper, we generalize a result recently obtained by the author. We characterize the cyclic vectors in $L_{a}^{p}\,\left( \mathbb{C},\,\phi \right)$ . Let $f\,\in \,L_{a}^{p}\,\left( \mathbb{C},\,\phi \right)$ and $fC$ be contained in the space. We show that $f$ is non-vanishing if and only if $f$ is cyclic.

Keywords

47A1646J1546H25weightedLp spaces of entire functionscyclic vectors

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 51 , Issue 3 , 01 September 2008 , pp. 378 - 385
Copyright
Copyright © Canadian Mathematical Society 2008

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