| THE CODIMENSION FORMULA ON QUASI-INVARIANT SUBSPACES OF THE FOCK SPACE |
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| 引用本文： | HOU Shengzhao,HU Junyun. THE CODIMENSION FORMULA ON QUASI-INVARIANT SUBSPACES OF THE FOCK SPACE[J]. 数学年刊B辑(英文版), 2003, 24(3): 343-348 |
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| 作者姓名： | HOU Shengzhao HU Junyun |
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| 作者单位： | HOU SHENGZHAO HU JUNYUN Department of Mathematics，Zhejiang University，Hangzhou 310027，China. Department of Mathematics，Shanxi Teachers University，Linfen 041004，Shanxi，China.Institute of Mathematics，Jiaxing College，Jiaxing 314001，Zhejiang，China. |
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| 摘 要： | Let M be an approximately finite codimensional quasi-invariant subspace of the Fock space. This paper gives a formula to calculate the codimension of such spaces and uses this formula to study the structure of quasi-invariant subspaces of the Fock space. Especially, as one of applications, it is showed that the analogue of Beurling's theorem is not true for the Fock space L_a~2 in the case of n > 2.
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| 关 键 词： | 余维数公式 拟不变子空间 Fock空间 Beurling定理 Siegel-Bargmann空间 整函数 应用 |
| 收稿时间： | 2025-02-02 |
The Codimension Formula on Quasi-Invariant Subspaces of the Fock Space |
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| HOU Shengzhao and HU Junyun. The Codimension Formula on Quasi-Invariant Subspaces of the Fock Space[J]. Chinese Annals of Mathematics,Series B, 2003, 24(3): 343-348 |
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| Authors: | HOU Shengzhao and HU Junyun |
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| Affiliation: | 1. Department of Mathematics, Zhejiang University Hangzhou,310027;Department of Mathematics, Shanxi Teachers University, Linfen 041004, Shanxi, China
2. Institute of Mathematics, Jiaxing College, Jiaxing 314001, Zhejiang, China |
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| Abstract: | Let M be an approximately finite codimensional quasi-invariant subspace of the Fock space. This paper gives a formula to calculate the codimension of such spaces and uses this formula to study the structure of quasi-invariant subspaces of the Fock space. Especially, as one of applications, it is showed that the analogue of Beurling's theorem is not true for the Fock space L_a~2 in the case of n > 2. |
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| Keywords: | Codimension formula Quasi-invariant subspaces Fock space |
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