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| 摘要: |
| 对α > 0，本文主要研究了复平面上的加权Fock空间Fα2上的自伴算子和线性算子的测不准原理.利用泛函分析中的一般性原理，在Fα2上构造了两个线性算子Tf=f'/α和T*=zf.进一步，构造了满足条件的两个自伴算子A和B，使得[A，B]为恒等算子的常数倍，得到了Fα2上更精确的算子的测不准原理形式，其中T*是T的对偶算子，[A，B]=AB-BA为A和B的换位置.本文的结果推广并完善了屈非非和朱克和在文献[1]和[2]中的结果. |
| 关键词: 加权Fock空间 测不准原理 线性算子 自伴算子 高斯测度 |
| DOI： |
| 分类号:O174.5 |
| 基金项目:Supported by National Natural Science Foundation of China (11561012; 11861024). |
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| FURTHER DISCUSSION ON UNCERTAINTY PRINCIPLES FOR THE α-FOCK SPACE Fα2 |
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PAN Wei-ye,YANG Cong-li,ZHAO Jian
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| Abstract: |
| In this article, for α > 0, we characterize several versions uncertainty principles of self-adjoint operators and linear operators for the α-fock space Fα2 in the complex plane. By using the general result from functional analysis, we find two linear operators Tf=f'/α and T*=zf to construct two self-adjoint operators A and B such that[A, B] is a scalar multiple of the identity operator on Fα2, and obtain some more accurate results about the uncertainty principles for the α-fock space Fα2, where T* is the adjoint of T,[A, B]=AB -BA is the commutator of A and B, which extends and completes the results of Qu[1] and Zhu[2]. |
| Key words: α-fock space uncertainty principles linear operators self-adjoint operators Gaussian measure |
