Cyclic vectors in the Fock space over the complex plane

被引：11

作者：

Izuchi, KH ^{[1
]}

机构：

[1] Niigata Univ, Grad Sch Sci & Technol, Niigata 9502181, Japan

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2005年 / 133卷 / 12期

关键词：

Fock space; entire function; cyclic vector;

D O I：

10.1090/S0002-9939-05-07938-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we characterize the cyclic vectors in the Fock space over the complex plane. We prove that a function f(z) is cyclic in the Fock space if and only if f(z) is a nonvanishing function in L-2 alpha(C).

引用

页码：3627 / 3630

页数：4

共 9 条

[1]

[Anonymous], 2003, Analytic Hilbert modules

[2]

Berenstein C.A., 1991, Complex Variables

[3] A Beurling-type theorem for the Fock space [J].

Chen, XM ;

Hou, SZ .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2003, 131 (09) :2791-2795

[4] Analytic Hilbert spaces over the complex plane [J].

Chen, XM ;

Guo, KY ;

Hou, SZ .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2002, 268 (02) :684-700

[5]

Garnett J.B., 1981, BOUNDED ANAL FUNCTIO

[6] Invariant subspaces, quasi-invariant subspaces, and Hankel operators [J].

Guo, KY ;

Zheng, DC .

JOURNAL OF FUNCTIONAL ANALYSIS, 2001, 187 (02) :308-342

[7]

Hedenmalm H., 2000, Theory of Bergman spaces, DOI DOI 10.1007/978-1-4612-0497-8

[8]

Hoffman K, 1962, BANACH SPACES ANAL F

[9]

Rudin Walter, 1974, Higher Mathematics Series

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