Geodesic
Cyclic Vectors in Some Weighted Lp Spaces of Entire Functions
Canadian mathematical bulletin, Tome 51 (2008) no. 3, pp. 378-385

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CMB-2008-038-9
Mots-clés : 47A16, 46J15, 46H25, weighted, Lp spaces of entire functions, cyclic vectors 
Izuchi, Kou Hei. Cyclic Vectors in Some Weighted Lp Spaces of Entire Functions. Canadian mathematical bulletin, Tome 51 (2008) no. 3, pp. 378-385. doi: 10.4153/CMB-2008-038-9
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[BG] Berenstein, C. and Gay, R., Complex Variables. Graduate Texts in Mathematics 125, Springer-Verlag, New York, 1991. Google Scholar

[BS] Brown, L. and Shields, A. L., Cyclic vectors in the Dirichlet space. Trans. Amer.Math. Soc. 285(1984), no. 1, 269–303. Google Scholar

[CG] Chen, X. and Guo, K., Analytic Hilbert Modules. CRC Research Notes in Mathematics 433, Chapman & Hall/CRC, Boca Raton, FL, 2003. Google Scholar

[CGH] Chen, X., Guo, K., and Hou, S., Analytic Hilbert spaces over the complex plane. J. Math. Anal. Appl. 268(2002), no. 2, 684–700. Google Scholar

[Gar] Garnett, J. B., Bounded Analytic Functions. Pure and Applied Mathematics 96, Academic Press, New York, 1981. Google Scholar

[GW] Garling, D. J. H. and Wojtaszczyk, P., Some Bargmann spaces of analytic functions. In: Function Spaces. Lecture Notes in Pure and Appl. Math. 172, Dekker, New York, 1995, pp. 123–138. Google Scholar

[GZ] Guo, K. and Zheng, D., Invariant subspaces, quasi-invariant subspaces, and Hankel operators. J. Funct. Anal. 187(2001), no. 2, 308–342. Google Scholar

[HKZ] Hedenmalm, H., Korenblum, B., and Zhu, K., Theory of Bergman Spaces. Graduate Texts in Mathematics 199, Springer-Verlag, New York, 2000. Google Scholar

[Izu] Izuchi, K. H., Cyclic vectors in the Fock space over the complex plane. Proc. Amer.Math. Soc. 133(2005), no. 12, 3627–3630. Google Scholar

[MMO] Marco, N., Massaneda, X., and Ortega-Cerdà, J., Interpolating and sampling sequences for entire functions. Geom. Funct. Anal. 13(2003), no. 4, 862–914. Google Scholar

[OS] Ortega-Cerdà, J. and Seip, K., Beurling-type density theorems for weighted Lp spaces of entire functions. J. Anal. Math. 75(1998), 247–266. Google Scholar

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