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2017 Cyclic vectors in Fock-type spaces of single variable
Hansong Huang, Kou Hei Izuchi
Nihonkai Math. J. 28(2): 117-124 (2017).

Abstract

This paper mainly considers cyclic vectors in the Fock-type spaces $ L_{a,\alpha}^{p,s }(\mathbb{C} )$ $(\alpha>0,p\geq 1, s>0)$ which consists of all entire functions $f$ such that $|f|^p$ is integrable with respect to the measure $\exp(-\alpha |z|^s) dA(z).$ The case of $s$ not being an integer was done in [9], where cyclic vectors are exactly those non-vanishing entire functions in $ L_{a,\alpha}^{p,s }(\mathbb{C} )$. In this paper it is shown that for each positive integer $s$, a function $f$ is cyclic in $ L_{a,\alpha}^{p,s }(\mathbb{C} )$ if and only if $f$ is non-vanishing and $f \mathcal{C} \subseteq L_{a,\alpha}^{p,s }(\mathbb{C} )$, where $ \mathcal{C} $ denotes the polynomial ring. Moreover, the condition that $f \mathcal{C} \subseteq L_{a,\alpha}^{p,s }(\mathbb{C})$ can not be dropped.

Acknowledgment

The authors are quite grateful to the referee for many valuable suggestions that make this paper more readable.

Citation

Download Citation

Hansong Huang. Kou Hei Izuchi. "Cyclic vectors in Fock-type spaces of single variable." Nihonkai Math. J. 28 (2) 117 - 124, 2017.

Information

Received: 1 May 2017; Revised: 10 June 2017; Published: 2017
First available in Project Euclid: 26 April 2018

zbMATH: 06873764
MathSciNet: MR3794320

Subjects:
Primary: 47A16
Secondary: ‎46J15

Keywords: cyclic vectors , Fock-type spaces

Rights: Copyright © 2017 Niigata University, Department of Mathematics

Vol.28 • No. 2 • 2017
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